UNIVERSITY OF MUMBAI

Post Graduate Diploma in Applied Statistics with Software

And

Post Graduate Diploma in

Actuarial Science

2

FROM THE HEAD OF THE DEPARTMENT

The field of statistics addresses how to collect, analyze and interpret collected data. There is growing demand for highly skilled statisticians in the 21st century in many fields including government, banking sector, health sciences, agricultural sciences, business, and social sciences and in other sciences also.

In these fields large volume of data is generated every day. Statistical

software’s are playing vital role into processing, management and analysis of huge collected data. Now a day, statistics is playing important role in creation of knowledge.

The course mainly focuses on how to train students to solve real life

problems using statistical software. These courses will benefit students for shaping their future in the field of data analysis. I wish you all the best for new career.

Dr. Santosh P. Gite

Head Department of Statistics

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Statistics: Statistics is all pervasive. It touches every aspect of life, research and business.

jaatsya ih Qa`uvaa saM#yaa

Qa`uvaa saM#yaa maRtsya ca

tsmaadpirhaya-o|qa-o

saM#yaaSaasHaM pzamyahma\

From birth to death statistics is associated with human being.

Statistics is the development and application of techniques involved with design of

investigation, summarization and inference from results of investigation to population

from which results are derived. Statistics offers a rational theory in context of

uncertainty with the central aim of characterizing how an individual should act in order to

avoid certain kinds of undesirable behavioral inconsistencies.

Twenty first century experiences information explosion. To manage this information we

need knowledge workers. Statistics will help these knowledge workers to draw accurate

conclusions in all the fields including health, psychology, ecology, politics, music,

lifestyle choices etc. etc. and enhance the quality of life.

Department of Statistics: Sixty years back renowned professor and great visionary Prof. M. C. Chakrabarti

founded the department of Statistics. It is the oldest and most recognized teaching and

research institute in the country. It offers post graduate course M.A. / M.Sc., M.Phil. and

Ph.D. programs in Statistics. It has close interaction with industry through its executive

development programs.

The department has 5 core and visiting faculty members besides dozens of industry

experts delivering lectures on various topics.

To live up to its reputation of excellent teaching and research department, we had

launched two new programs, first of their kind in the country—―Post graduate Diploma

in Applied Statistics with Software” and “Post Graduate Diploma in Actuarial

Science”

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POST GRADUTE DIPLOMA IN APPLIED STATISTICS WITH SOFTWARE

(PGDASS) The Course: Department of Statistics, University of Mumbai has specially designed a one-year Post

Graduate Diploma in Applied Statistics with Software for students and professionals

who wish to make a successful and rewarding career in business and research.

Focus: The focus of the course will not be on statistics or mathematics; but on applications of

these techniques for taking better business and research decisions. All the techniques

required in business and research to take sound decisions will be covered in the course.

Besides, the latest software like SAS and SPSS will be used in the course to solve all

the business and research problems. Students will be given hands-on training on

computers for all the techniques.

The course focuses more on practical aspects of the problems and therefore all the

techniques will be discussed with real-life, research and industry data. The course,

besides statistics and mathematics, highlights the importance of good communications

and will expose students to the latest techniques of communications to become a

successful professional in any field.

Faculty: Department of Statistics is very choosy about the faculty that will teach the course. After

careful deliberations the Department of Statistics has drawn up a list of highly qualified,

experienced and expert professors and industry professionals.

Projects: To make the course more relevant to business and research, students will be

undertaking industry and corporate projects under the expert guidance of the faculty.

Assessment: The assessment of students will be made continuously on the basis of class tests,

presentations, case studies and group-projects. There will be External Examination at

the end of each semester.

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Papers: There will be eight papers including a project besides interim projects in each subject.

The titles of the papers are as follows:

1. Basic Statistics

2. Marketing Research

3. Regression and Linear Models

4. Decision Making and Forecasting

5. Six Sigma and Statistical Process Control

6. Medical Statistics

7. Multivariate Techniques.

8. Communication Skills and Project

Facility:

To deliver the best measuring the industry and research standards, students will be

provided excellent facilities during the course as:

Networking of computers and Internet.

The latest software like SAS, MINITAB, SPSS and R.

LCD Projector and white boards.

Air conditioned computer lab

Audio system.

Placement: After completion of the course, assistance in placement will also be offered to students

to get better placements in the corporate and research world.

Industries that would absorb these students are pharmaceuticals and healthcare,

consultancy firms, Marketing Research Agencies, Financial companies, Insurance

companies, Consumer Durable companies, FMCG companies etc.

Eligibility: Any graduate from Mumbai University or any other recognized university.

Admissions are strictly on the basis of entrance test. Students with B.Sc. (Statistics)

major are exempted from entrance test.

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Number of Seats : 50 (Minimum number of students to be admitted should be 15 in

order to conduct the course in that academic year.)

Duration of Course:

One year Full time Course. Timings will be intimated later. ---------------------------------------------------------------------------------------------------------------------

“POST GRADUATE DIPLOMA IN ACTUARIAL SCIENCE” (PGDAS)

The Course: The department has formulated another unique course keeping in mind the ever

growing demand of insurance and risk management industry. The course will develop

world-class actuaries with focus on product design, policy pricing and assets-liability

management in the areas of insurance, pension, investment, banking and healthcare

management.

The Faculty: To live to its reputation of having excellent, qualified and experienced faculty with

decades of expertise, the department has drawn up a list of faculty who would deliver

the best for the course.

Assessment: The assessment of students will be made continuously on the basis of assignment and

class tests for internal assessment. There will be External Examination at the end of

each semester.

Papers:

There will be eight papers. The titles of the papers are as follows:

1. Financial mathematics

2. Finance and Financial reporting

3. Probability and Mathematical Statistics

4. Business Economics

5. Contingencies

6. Statistical Methods

7. Statistical Models

8. Financial and Statistical Economics

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Placement: After successful completion of the course, assistance will be offered to the students to

get placements in the corporate and research world.

Industries that would absorb these students are Consultancy firms, Financial

companies, Insurance companies, Banks etc.

Eligibility: Any graduate from Mumbai University or any other recognized university.

Admissions are strictly on the basis of entrance test, Students with B.Sc. (Statistics)

major are exempted from entrance test.

Number of Seats : 50 (Minimum number of students to be admitted should be 15 in

order to conduct the course in that academic year.)

Duration of Course: One year Full time Course. Timings will be intimated later. ---------------------------------------------------------------------------------------------------------------------

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POST-GRADUATE DIPLOMA IN ACTUARIAL SCIENCE

Introduction:

Actuaries are statisticians involved in number crunching and handling tons of mortality and other statistics to device the correct pricing of insurance policies. As an actuary, he has the opportunity to work in a wide number of areas in life insurance, general insurance, reinsurance, pension funds, risk management and so on. The work profile includes product design, policy pricing and asset-liability management among others.

The Insurance Regulatory and Development Authority (IRDA) mandates that life insurance companies must have at least one appointed actuary, while general insurers can meet their actual needs with the help of consultants. Over the next three years, industry sources expect the number of actuaries in private sector life insurance to double. Consultants feel that over five years, the number can reach 600 in life and about 300 in non life insurance. Demand for actuaries is likely to intensify as new entrants look at India and some expatriates in existing companies return home. While the opportunities for young, experienced students are currently good, long-term demand will come at the experienced, senior, appointed actuary level. Fee Structure: Rs. 40,000 per year * Rs. 1,000 Examination fee per term. Rs. 800 P.G. Registration Fee. *Note: If there is a change in the fees then the excess amount will be collected

afterwards.

Scheme of Examination: The evaluation of the performance of a student in each paper shall be based upon both internal assessment and external examination. The external examination will be held only once at the end of an academic term. The external examination will consist of EIGHT papers each of THREE hours.

Subject Title Internal External Total

Paper I Financial Mathematics 40 60 100

Paper II Finance and Financial Reporting 40 60 100

Paper III Probability and Mathematical Statistics 40 60 100

Paper IV Business Economics 40 60 100

Paper V Contingencies 40 60 100

Paper VI Statistical Methods 40 60 100

Paper VII Statistical Models 40 60 100

Paper VIII Finance and Statistical Economics 40 60 100

First term will consist of first four papers & Second term will consist of next four papers. Internal Exam will be held only once in each term.

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Paper –I: FINANCIAL MATHEMATICS

1. Interest rates and factors

2. Level annuities

3. Varying annuities

4. Non-annual interest rates and annuities

5. Project appraisal and loans

6. Financial instruments

7. Duration, convexity and immunization

8. The term structure of interest rates

9. Stochastic interest rates

Reference Books:

1. Baxter, Robert. Finance Mathematics, Medford, OR:Baxter

2. Hart, W. L. Mathematics of Investment, Lexington, MA:D.C.Health, 1975, Fifth

edition.

Instructional Materials, 1992. Sixth Edition Revised and Expanded. 3. Karatzas, loannis and Shreve, Steven E.,Methods of Mathematical Finance, New

York, NY:Springer, 1998.

4. Kellison, Stephen G. The theory of Interest, Homewood, IL: Richard D. Irwin,

1970, 1990. Second Edition.

5. Martin, Peter G. and Burrow, Michael. Applied Financial Mathematics, New York,

NY; Sydney: Prentice Hall, 1991.

6. McCutcheon, J. J. and Scott, W. F. An Introduction to Mathematics of Finance

7. Roman, Steven. The Mathematics of Finance, Irvine, CA: Innovative Textbooks,

1993.

8. Ruckman Chris & Francis Joe : Financial Mathematics : A practical guide for

Actuaries and other Business professionals

9. UK Institute of Actuaries core reading for the subject CT1 financial mathematics

10. Watsham, Terry J. and Parramore, Keith. Quantitative Methods in Finance,

London;Boston, MA:International Thomson Business Press, 1997. First Edition.

Paper-II: FINANCE AND FINANCIAL REPORTING

1. Key principles of finance

2. The basic construction of accounts of different types and principal features of the

accounts of company

3. Interpretation of the accounts of a company or a group of companies and

limitations of such interpretation

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4. The characteristics of the principal form of financial instrument used by

companies

5. Definition of company’s cost of capital and weighted average cost of capital

6. Factors to be considered by company when deciding on its capital structure and

dividend policy

7. Financial techniques used in the assessment of capital investment project

8. Definitions & Residential Status under Income Tax Act, 1961

9. Heads of Income under Income Tax Act, 1961

10. Basic principles of personal taxation under Income Tax Act, 1961

11. Basic principles of company taxation under Income Tax Act, 1961

Reference Books Foreign Authors

1. Brealey, Richard A and Myers, Stewart C, principles of corporate finance.

2. Brigham,Eugene F Houston, Joel F, Fundamentals of financial management

3. Holmes, Geoffrey and Sugden Alan, interpreting company reports and accounts

4. Samuels, J.M.; Wilkes, F.M; Bray Shaw, R.E. management of company

5. UK Institute of Actuaries Core Reading for subject CT2 Finance and Financial

Reporting

Indian Authors 1. Advanced Accountancy – S.N. Maheshwari ISBN 0706999118

2. Advanced Accounts – M.C. Shukla, T.S. Grewal

3. Financial Accounting – P.C. Tulsian

4. Financial Management – M.Y. Khan, P.K. Jain ISBN 9780070656147

5. Financial Management – Prasanna Chandra ISBN 9780070656659

6. T.N. Manoharan – Tax

7. Vinod Singhania – Tax

Paper III: PROBABILITY AND MATHEMATICAL STATISTICS 1. Main features of a data set (exploratory data analysis)

2. Concepts of probability

3. Concepts of random variable, probability distribution, distribution function,

expected value, variance and higher moments

4. Probability generating function, moment generating function, cumulant

generating function and cumulant.

5. Basic discrete and continuous distributions

6. Concept of independence, jointly distributed random variables and conditional

distributions, use of generating functions

7. Central limit theorem and its applications

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8. Concepts of random sampling, statistical inference and sampling distribution

9. Methods of estimation and properties of estimators

10. Confidence intervals for unknown parameters

11. Testing of hypotheses

12. Correlation and regression analysis

13. Concept of analysis of variance

14. Concepts of conditional expectations and compound distribution

Reference books: 1. Hogg, R., and A. Craig: Introduction to Mathematical Statistics, The

Macmillan Company, New York, 1959. Mathematical Statistics with applications, Duxbury, 2002.

2. Mood Alexander M., Graybill Franklin A.:(1950) Introduction to the theory of StatisticsSecond Edition,McGraw –Hill Book Company Inc.

3. Rohatgi V. K. and A. K. MD. Ehsanes Saleh: An introduction to probability theory abd mathematical statistics, 2nd ed. John Wiley and Sons, 2001.

4. UK Institute of Actuaries core reading for reading for subject CT3 Probability and mathematical Statistics

5. Wackerly D. D; Mendenhall III, and Scheffer, R. L.

Paper IV: BUSINESS ECONOMICS 1. Relevance of economics to the world of business.

2. The workings of competitive markets.

3. Consumer demand and behaviour.

4. Firm’s decision on product selection and marketing and advertising strategies.

5. Production function, costs of production, revenue and profit in order to

understand a firm’s price and output decisions.

6. Profit maximisation under perfect competition, imperfect competition and

monopoly.

7. Role of a firm’s growth strategy on its profitability and survival.

8. Pricing strategies that firms can adopt.

9. Reasons for government intervention in the market.

10. Relationship between the government and the individual firm.

11. Globalisation and multinational business.

12. The importance of international trade.

13. The macroeconomic environment of the business.

14. The Balance of payments and concept of exchange rate determination.

15. The role of money and interest rates in the economy.

16. Determinants of level of business activity and how it affects unemployment

and inflation.

17. Macroeconomic policies impact on businesses.

18. Supply side policies impact on businesses.

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Reference Books:

1. Business economics.Perman, R.; Scouller, J. Oxford University Press, 1999.

2. Economics.Begg, D. K. H.; Fischer, S.; Dornbusch, R. 9th ed. McGraw-Hill, 2008.

3. Economics.Krugman, P.; Wells, R.; Graddy, K. European ed. Worth, 2007.

4. Economics.Lipsey, R. G.; Chrystal, K. A. 11th ed. Oxford University Press, 2007

5. Economics.Mankiw, N.G.; Taylor, M. P. Thomson, 2006 6. Economics. Parkin, M.; Powell, M.; Matthews, K. 7th ed. 7. Economics.Sloman, J. 6th ed. FT Prentice Hall, 2006. ISBN: Pearson

Education, 2007. 8. Economics for business.Begg, D. K. H.; Ward, D. 2nd ed. McGraw-Hill,

2007. 9. Essentials of economics.Sloman, J. 4th ed. FT Prentice Hall, 2006. 10. Institute of Actuaries core reading for the subject CT7 economic

Paper V: CONTINGENCIES 1. Simple assurance and annuity contracts

2. Practical methods of evaluating expected values and variances of the simple

contracts

3. Life Tables.

4. Variable benefits and annuities.

5. Gross premiums and reserves.

6. Joint life and last survivor status.

7. Multiple decrements.

8. Profit Testing

9. Factors affecting mortality.

Reference Books: 1. Benjamin, Bernard and Pollard, John H., The analysis of mortality and

other actuarial statistics. 3rd ed. Institute of Actuaries and Faculty of Actuaries, 1993

2. Booth, P. M. al., Modern actuarial theory and practice, Chpaman &Hall,1999

3. Bowers, Newton L et al., Actuarial Mathematics 2nd ed. Society of Actuaries, 1997.

4. Gerber, H. U.,Life insurance mathematics 3rd ed. Springer , Swiss Association of Actuaries, 1997

5. Haberman, S. and Pitacco, E., Actuarial models for disability insurance Cahpman & Hall, 1999

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6. Life Contingencies – A guide for the Actuarial Student – by Robert W Batten

7. Life Contingencies- by C. W. Jordon (Chester Wallance Jordon) 8. Neill,Alistair, Life contingencies. Heinemann, 1977 9. Theory of Interest and Life Contingencies with Pension Applications: A

problem solving approach- by Michael M. Parmenter 10. UK Institute of Actuaries Core Reading for subject CT5 contingencies.

Paper VI: STATISTICAL METHODS 1. Claims Reserving and Pricing with Run-off Triangles

2. Loss Distribution

3. Risk Theory

4. Ruin theory

5. Credibility Theory

6. No claim discounting in Motor Insurance

7. Generalized Linear Model

8. Decision and Game Theory

9. The main concepts underlying the analysis of time series models

10. Concepts of ―Monte Carlo‖ simulation

Reference Books: 1. Bolan Philip J. – Statistical and Probabilistic Methods in Actuarial Science

Chapman and Hall/CRC 2. Box G.E.P. and Jenkin’s : Time series analysis forecasting and control 3. Morgan B.J.T. Elements of simulation, Chapman & Hall, 1995. 4. UK Institute of Actuaries core reading for subject CTVI statistical methods 5. Ross S. M. Introduction to Probability Models- 7th Edition

Academic Press/Harcourt 2000

Paper VII: STATISTICAL MODELS 1. Principles of Stochastic Processes, their classification into different types

2. Markov Chains

3. Two state Markov Model

4. General Markov Model

5. Markov Jump Process

6. Survival Models and life tables

7. Estimating lifetime distribution function

8. The Cox regression model

9. The binomial and poison Model

10. Exposed to risk

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11. Graduation and Statistical tests

12. Methods of graduation.

13. Ross Models: From Data to decisions (third edition)(2008),Klugman S.A.,

Panjer H.H.,and Willmot, G.E.

Reference Books: 1. Bain L. J.: Statistical Analysis of reliability and life testing models 2. Bhat Narayan U. & Miller Gregory K (2002): Elements of applied

Stochastic Processes Third edition, John Wiley and sons 3. Durrett R.: Essentials of Stochastic Processes 4. Kulkarni V. G.: Modelling and analysis of stochastic systems. 5. Medhi J.: Stochastic Processes, Wiley Eastern Ltd, 2nd Edition 1994 6. Ross S. M.: Introduction to Probability Models 7. Smith P. J. : Analysis of failure and Survival data 8. UK Institute of Actuaries core Reading for Subject CT4 Models

Paper VIII: FINANCIAL AND STATISTICAL ECONOMICS 1. Mechanics of Future Market &Hedging Strategies

2. Interest Rate

3. Determination of Forward and Future Prices

4. Interest Rate Futures, Swaps

5. Mechanics of options Markets

6. Properties of Stock Options, Trading Strategies involving options

7. Binomial Trees, Wiener Procedures and Ito’s Lemma

8. The Black-Scholes-Metron Model

9. Basic Numerical Procedures, Credit Risk

10. Martingales and Measures, Interest Rate Derivatives: the standard market

models

Reference Books:

1. Elton Edwin J. and Gruber Martin J. (1997): Modern Portfolio Theory and

Investment analysis 7th edition, John Wiley & Sons 2. Hull John C. (2006): Options, Future and other Derivatives 8th Edition 3. Panjer Hary H. (1998): Financial Economics

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Standard of Passing:

1. A candidate securing a minimum of 200 out of 400 marks with a minimum of

40 marks in each of the four papers consisting of internal and external

examination taken together will be declared to have passed in that

examination.

2. If in a paper a candidate secures minimum of 50% marks consisting of

internal and external examination taken together, will be exempted from that

paper.

3. A candidate will be declared to have passed the examination if he/she passed

in all papers.

4. A candidate will be awarded the following Grades on the basis of percentage

of total marks obtained by the candidate in one or more attempt (s).

Percentage Grade

50 below 60 C

60 below 70 B

70 below 80 A

80-100 A+

5. A registration of the candidate is valid only for three years for the course.

After the three years he/she will have to register again.

*******************************

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POST-GRADUATE DIPLOMA IN APPLIED STATISTICS WITH SOFTWARE Introduction: Statistics has become a vital tool of data analysis and valid inference in almost all

fields in the present era. Statistical techniques are applied in Finance, Insurance,

Marketing, Manufacturing, Social Sciences, Health Sciences and Software Designing

etc. A huge volume of data is generated in these fields every day. Processing and

Management of this data has become a vital need of the hour. This necessitates a

pertinent exposure to various Statistical Techniques to all the users.

Processing and management of this voluminous data using computerized

Statistical packages has become essential in the current era.

Over the next three years industry sources expect the number of statistician in

Private Sector to double. Demand for statistician is likely to intensify as new entrants in

clinical trials and pharma industry look at India.

Fee Structure: Rs. 40,000 per year * Rs. 1,000 Examination fee per term. Rs. 800 P.G. Registration Fee. *Note: If there is a change in the fees then the excess amount will be collected afterwards.

Scheme of Examination: The evaluation of the performance of a student in each paper shall be based upon both

internal and external examination. The external examination will be held only once at

the end of an academic term. The external examination will consist of EIGHT papers

each of THREE hours.

Subject Title Internal External Total

Paper I Basic Statistics 40 60 100

Paper II Marketing Research 40 60 100

Paper III Regression and Linear Model 40 60 100

Paper IV Decision Making and Forecasting 40 60 100

Paper V Six sigma &Statistical Process Control

40 60 100

Paper VI Medical Statistics 40 60 100

Paper VII Multivariate Techniques 40 60 100

Paper VIII Communication Skills , Accounting & Project

100 --- 100

First term will consist of first four papers & Second term will consist of next four papers & project work. Internal Exam will be held only once in each term.

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Detailed syllabus for the subject:

PAPER I: BASIC STATISTICS

1. Exploratory Data Analysis

2. Concepts of Probability

3 Concepts of Random Variable, Probability distribution, Distribution Function,

Expected Value, Variance and Higher Moments.

4 Probability generating function, moment generating function, cumulate

generating function and cumulant.

5 Basic discrete and continuous distributions.

6 Concepts of independence, jointly distributed random variables and

conditional distributions, use of generating functions.

7 Central limit theorem and its application

8 Concepts of random sampling, statistical inference and sampling

distribution.

9 Methods of estimation and properties of estimators.

10 Confidence intervals for unknown parameters.

11 Testing of hypothesis

12 Concepts of conditional expectation and compound distribution

13 Simulation

Reference Books:

1. Anderson David R., Sweeny Dewis J. and Williams Thomas A (2004):

Statistics for business and economics. 2. Hogg, R., and A. Craig: Introduction to Mathematical Statistics, The

Macmillan Company, New York, 1959. 3. Levin Richard I and Rubin Deavid S (1994) Statistics for management.

Mathematical Statistics with application. 4. Rohatgi V. K. & A. K. MD. Ehsanes Saleh (2001): An Introduction to

probability theory and Mathematical Statistics Second Edition. 5. Wackesly D.D,Mondonhall III, William and Scheffer R.

L.(2002):Mathematical Statistics with applications 6. Mood Alexander M., Graybill Franklin A.:(1950) Introduction to the theory

of StatisticsSecond Edition,McGraw –Hill Book Company Inc.

PAPER II: MARKETING RESEARCH

1. Definition of marketing research and market research, need for marketing

research, requirement of good marketing research, manager researcher

relationship, competitive and complex nature of Indian markets, role of

research in new product development, packaging, branding, positioning,

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distribution and pricing, ethics in Business Research.

2. Steps in marketing Research.

3 Techniques for identifying management problem and research problem.

4. Meaning & types of research designs-exploratory, descriptive and casual.

5. Exploratory research designs, Sampling & data collection methods

6. Causal research designs: Data collection methods

7. Descriptive research design: Sampling methods, Types of scales,

questionnaire design

8. Preparations research proposal

9. Objectives and data needs for consumer research.

10 Objectives and data needs for product research.

11. Objectives and data needs for pricing research

12. Objectives and data needs for advertising research.

13. Consumer segmentation techniques: Chi-square test of independence,

Cluster analysis

14. Customer discriminating technique: Discriminant analysis

15. Product positioning techniques: Snake chart, Benefit structure analysis,

Multi-dimensional scaling technique, Factor analysis

16. CHi-squared Automatic Interaction Detector (CHAID)

17. New product development technique: Conjoint analysis

18. Report writing

Reference Books:

1. Kinnear Thomas C and Taylor James R. (1995) Marketing Research: An applied Approach

2. Green Paul E., Tull Donalds, Albaum Gerald (1988): Research for Marketing Decision. 3. Nargundkar Rajendra(2003), Marketing Research Text & Cases. 4. David A. Aaker(2004) Marketing Research 5. Malhotra Naresh (2006) Marketing Research

An applied orientation and SPSS 14.0 student CD. 6. Burns C. Alwin & Bush Ronald(2006): Marketing Research with SPSS 13.0 7. Boyd Harper W. Jr. Westfall Ralph, Stasch Stanley F. (1977)

Marketing Research: Text & Cases 8. Harvard Business Review: Select Articles on Marketing Research.

PAPER III: REGRESSION AND LINEAR MODEL

1. Simple linear regression

2. Multiple linear regression

3. Regression diagnostics

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4. Transformation of variable

5. Qualitative Variables as predictors

6. Analysis of collinear data

7. Logistic regression

8. Stepwise regression

9. ONE WAY ANOVA

10. TWO WAY ANOVA

11. Multiway ANOVA and Nested Analysis

12. Comparison of individual means

13. Analysis of covariance

14. One Way Random effect model

15. Two way Mixed Model

Reference Books: 1. Chatterjee Samprit, Hadi Ali S., Price Betram (2000): Regression Analysis by

Example Third Edition A Wiley Interscience Publication John-Wiley and Sons 2. Draper Norman R., Smith Harry (2003): Applied Regression Analysis Third

Edition 3. Kshirsagar Anant M. (1983): A course in Linear Models 4. Seber George A. F. (2003) Linear Regression Analysis 5. Dielman Terry E. (2004) Applied Regression analysis: A second course on

Business and Economics Statistics. 6. Chatterjee Samprit, Handcock Marks, Simonoff Jeffrey (1994) A Caselook for

a list course in Statistics and data Analysis. 7. Design and analysis of experiments (2010) 7th ed. Douglas C. Montgomery,

Wiley India Pvt Ltd. 8. Design and analysis of experiments classical and regression approach with

SAS, Onyiah L.C. (2008) Chapman and Hall/CRC.

PAPER IV: DECISION MAKING AND FORECASTING

1. Basic concepts of Forecasting and Decision Making.

2. Quantitative techniques of Decision Making: Decision Tree, Break-

even analysis, Investment appraisal, Critical Path analysis.

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3. Qualitative techniques of Decision making : SWOT analysis, PESTEL

analysis, Six Thinking Hats Technique, Human Mindset Affecting

Implementation of Decision.

4. Statistical Rules of Decision Making, Bayesian approach

5. Step by step process of Decision Making.

6. Quantitative Causal Techniques of Forecasting: Regression Model,

Econometric Model, Input Output Model, Leading Indicator Model,

Logistic Regression model.

7. Quantitative Time Series Techniques of Forecasting: Trend Projection

Models, Smoothing Techniques, Classical Decomposition Model, Box-

Genkins Model

8. Selection of right forecasting method.

9. Qualitative Methods of Forecasting: Delphi Method, Subjective

Probabilities Method, Market Research.

10. Decision Making under Uncertainty, Role of Probability Theory and

Statistical Techniques, Forecasting-based Decision Making.

11. Characteristics of Decision: Unstructured or Non-Programmable

Decisions, Structured or Programmable Decisions.

12. Quantitative Tools of Decision Making: Decision Tree, Break-even

analysis, Investment appraisal, Critical Path Analysis

13. Qualitative Tools of Decision Making: Qualitative Factors Influencing

Decision Making, SWOT Analysis, PESTEL Analysis, Six Thinking

Hats Technique, Human Mindset Affecting Implementation of Decision

14. Statistical Rules of Decision Making: Maximin Criterion, Maximax

Criterion, Minimax Regret Criterion, Laplace Criterion.

15. Bayesian Approach to Decision Making: Prior Analysis, Pre-posterior

Analysis, Posterior Analysis, Sequential Analysis.

16 Step by Step Process of Decision Making.

17. Inventory management and introduction, inventory control, costs in

inventory problems, Techniques of Inv. Control and with selective

control (ABC analysis, Usage rate and criticality)

18. Techniques of inv. Control and with known demand and E.O.Q with

uniform demand, prod. Runs of unequal length, with finite rate of

replenishment, Problem of E.O.Q with shortage

19. Techniques inv. Control and with uncertain demand and buffer stock

computation, stochastic problems and uniform demand.

20 Techniques inv. Control and with price discounts

21. Break even analysis, Marginal Costing

21

Reference Books: 1. Mayes Timothy R., Shack Todd. M(2006).: Financial Analysis with Microsoft

Excel. 2. Martin Mindy C., Hansen Steven M., Klingher Beth,(1996): Mastering Excel

2000 Premium Edition. 3. Spyros G Makrindakis Steyan C. Wheelwright Rob J. Hyndman: Forecasting:

Methods & Applications 4. Hanke,John E.,Reitsch Arthur G.,Wichern Dean W.: Business Forecasting 7th

Edition

PAPER V: SIX SIGMA AND STATISTICAL PROCESS CONTROL.

1 7 QC tools, 7 New QC tools

2 Control Charts for variables

3 Six sigma , Lean Sigma

4 Process and measurement system capability analysis

5 Factorial and Fractional factorial experiments for process design and

improvement

6 Response surface methods and designs

7 Taguchi techniques

8 Japanese System

9 ISO 9000

10 Project Planning

11 Statistics in software development process

Reference Books: 1. Montgomery Douglas C. (2004): Introduction to statistical quality control

Fourth Edition. 2. Phadke Madhav S. (1989): Quality Engineering Using Robust Design 3. Kaoru Ishikawa(1986): Guide To Quality Control Second Edition. 4. Genichi Taguchi ( 1991): Introduction to Quality Engineering:

Designing Quality into Products and Processes Second Edition. 5. Brassard Michael & Diane Riffer (1994): The Memory Jogger II 6. Harry Mikel & Schroeder Richard (1999): Six Sigma The Breakthrough

Management. 7. Pande Peter S., Neuman Robert P. & Cavanagh Rolana R.(2002): (Six

Sigma Way Team) An Implementation Guide for Process Improvement.

PAPER VI: MEDICAL STATISTICS

1 Phase I, II and III Clinical Trials

2 Randomization

3 Blinding and Placebos

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4 Sample size calculation

5 Nonparametric Tests: Fisher’s exact test, Wilcoxon Signed Rank test,

Wilcoxon Rank Sum test, Mann-WhitneyUtest, Kruskal-Wallis test.

6 Comparing more than two treatments.

7 Causality, Non-compliance and Intent-to-treat

8 Survival analysis in Phase III clinical trials

9 Early stopping of clinical trials

10 Multiplicity and interim analysis

11 Parallel and Crossover designs

12 Binary Response data, Categorical Data Analysis

13 Comparing Methods of measurements.

14 Meta analysis

15 Repeated measures analysis

Reference Books: 1. .Shoukri M. M., Pause C. A. (1999): Statistical Methods for Health Sciences

Second Edition. 2. Davis Charles S. (2002): Statistical Methods for the Analysis of Repeated

Measurements. 3. Finney D, J (1964): Statistical Method in Biological Assays. 4. Fleiss Joseph L.,Levin Bruce & Paik Myunghee Cho (2003): Statistical

Methods for Rates and Proportions 5. Dr. Fieller Nick (2007): Medical Statistics: Clinical Trials 6. Zhang Daowen (2007): Statistical Principles of Clinical Trials (Lecture Notes)

PAPER VII: MULTIVARIATE TECHNIQUES

1 The organization of Data

2 Applications of Multivariate Techniques.

3 Data Display and Pictorial Representation.

4 Assessing the Assumption on Normality

5 Detecting Outliers and Data Cleaning

6 Transformations to Near Normality

7 Hotelling’s T2 and Likelihood Ratio Tests

8 Confidence Regions and simultaneous Comparisons of Component

Means.

9 Large Sample Inferences about a Population Mean Vector

10 The Classical Linear Regression Model.

11 Principal Components

23

12 Factor Analysis

13 Cluster Analysis

14 Discrimination and Classification

15 Multi Dimensional Scaling

Reference Books:

1. Johnson, Richard A. & Wichern, Dean W(2007).: Applied Multivariate Statistical Analysis.

2. Seber, G.A.F(1984).: Multivariate observations 3. Bishop Yuonne M. M., Fienbeng S. E.,Holland P. W.(1975): Discrete Multivariate

Analysis Theory and Practice.

PAPER VIII Communication Skills, Accounting and Project Communication

Module I : COMMUNICATION SKILLS

1 Spoken & Written communication

2 Preparing and organizing a public speech: Topic selection, Research

Methods, Overcoming anxiety, arranging main points, Constructing

introductory and concluding remark; Development and delivering

informative-style and persuasive-style, speeches; Debating: Fundamentals

of debating, Premises and process of debate, Basic rules & language,

Building & processing cases, Rebuttal arguments, Timing, Roles of the

speakers, Judges & moderator; Debating style: Parliamentary, Academic,

Cross- examination informal and impromptu speaking excercises.

3 Politics & governance, Business, Social, Morals & ethics, Culture &

education, Law & order, Science & technology, Handling questions.

4 Personal communication, Business communication, Report Writing.

5 Fundamentals of Presentations: Effective presentation- understanding

effective presentation, understanding different types of presentation;

Planning presentations: Establishing objectives, Determining objectives,

Making realistic objectives;

6 Analysing audience, Selecting supporting material, Understanding the

types of supporting materials, Exploring retention & visual aids; Building

presentation: Developing introduction, Capturing attention of audience,

Organizing body of presentation, Creating conclusions, Closing

presentation; Presentation mechanism: Power point, Visual aids, Speaker

notes & footnotes, Reviewing presentations.

24

Reference Books: 1. Bahl Sushil (1996): Business Communication Today 2. C. S. Rayadu: Media & Communication Management. 3. Thrill V. John, Bovee Courtland (2004): Excellence in Business

Communication. 4. Nichols Ralph G., Leonard A. Stevens, Bartolome Fernando, Argyris Chris

(1999): Harvard Business Review on Effective Communication.

Module II: Accounting 1. Introduction to Accounting – Basic Accounting Terms, Need and

Importance of Book-keeping – Accounting 2. Conceptual Frame work of Accounting - Basic assumptions – Basic

concepts –Accounting Standards 3. Double entry system – Account – Golden rules of accounting. 4. Basic Accounting Procedures – Journal, Ledger, Trial Balance 5. Final Accounts - Trading account – Profit and loss account –

Balance sheet – Preparation of Final Accounts.vv Reference Books: 1. Advanced Accounts – M.C. Shukla, T.S. Grewal

2. Book Keeping and Accountancy – Choudhari, Chopde.

Module III : PROJECT

Students should carry out the project on Statistical Application based on data

Note: The entire course will be taught using Statistics Software such as R/SAS/SPSS/MINITAB.

25

Standard of Passing:

1. A candidate securing a minimum of 200 out of 400 marks with a minimum of 40 marks in each of the four papers consisting of internal and external examination taken together will be declared to have passed in that examination.

2. If in a paper a candidate secures minimum of 50% marks consisting of internal and external examination taken together, will be exempted from that paper.

3. A candidate will be declared to have passed the examination if he/she passed in all papers including project.

4. A candidate will be awarded the following Grades on the basis of percentage of total marks obtained by the candidate in one or more attempt (s).

Percentage Grade

50 below 60 C

60 below 70 B

70 below 80 A

80-100 A+

5. A registration of the candidate is valid only for three years for the course.

After the three years he/she will have to register again. 6. Internal examination will be held once and same marks will carry forward.

Fees: The fees prescribed for the One year Post-Graduate Diploma in Applied Statistics with Software and Post Graduate Diploma in Actuarial Science is Rs.40,800 each. (If there is a change in the fees then the excess amount will be collected afterwards.) In case a student wants to withdraw his/her admission, he/she has to apply at least one week before the commencement of the course. In such a case, administrative charges to the extent of 25% will be deducted as cancellation charges. After the commencement of the course no fees shall be refunded. Mode of Payment: Fees should be paid only by demand draft in favour of ―THE FINANCE AND ACCOUNTS OFFICER, UNIVERSITY OF MUMBAI‖ Payable at Mumbai.

26

HOW TO APPLY Brochure and application forms can be collected from the office of the Department of Statistics, University of Mumbai, Vidyanagari Campus, Tilak Bhavan Building, 2nd Floor for Rs. 400 at the above address before the last date specified.

ENTRANCE TEST Common Entrance test will be held for two courses. Questions will be based on the following topics:

1. Limits 7. Ratio and Proportions 2. Derivatives 8. Quadratic equations 3. Integrals 9. Matrics and determinant 4. Sequences and Series 10. Descriptive statistics 5. Simple and Compound Interest 11. Standard distributions 6. Permutation and Combination 12. Probability

The question paper will contain objective questions and short type questions to be answered in 90 minutes. IMPORTANT DATES TO BE REMEMBER

IMPORTANT DATES

Sr. No

Event Date

1 Last date of submission Test Form.

2 Date of Entrance Test

3 Announcement of Results

4 Registration of candidates in Merit List-I

5 Last date for submission of Registration form for merit list- I candidates

6 Registration of candidates in Merit List –II (If seats are balance)

7 Last date for submission of Registration form for merit list- II candidates (if any)

8 Probable Date of Commencement of Course

You can also refer the website for the above dates.

27

TEACHING FACULTY

Dr. Santosh Gite M.Sc. Ph.D. Dr. Gite is the Associate Professor and Head of the Department at the Department of Statistics, University of Mumbai. He has taught several courses for more than 15 years. He was a resource person for many workshops and refresher courses. He has published more than seven research papers in international journals. His research interest is Operation Research, Regression Analysis.

Dr. (Mrs.) Vaijayanti Dixit M.Sc. Ph.D. Currently she is Associate Professor at the Department of Statistics, University of Mumbai. She has taught several courses at the PG level for the last ten years. She had conducted training programs to Fractal Analytics ltd. and was a resource person for refresher courses. She had published eight papers in international journals. Her research interest is statistical inference.

Prof. Jitendra Tawde M.Sc. Heading Quality Assurance Department of Godfrey Philips India Ltd. He is co-opted member on Board of studies for statistics of Mumbai University. His expertise includes ISO systems & six sigma. He is one of the committee members who designed post graduate diploma course in applied statistics with software.

Dr. Alok Dabade M.Sc., M.Phil, Ph.D He is Assistant Professor in the Department from last three years. He has published more than seven research papers. He has taught several courses at the PG level from the last four years. His research interest is survival analysis.

28

Prof Seema C M.A., MPhil, NET, P.G. Rec. Ms. Seema C is currently working as Assistant Professor at the Department of English in SIES College of Arts, Science and Commerce. She is a Gold Medallist with 10 years of teaching experience. She has taught at various faculties including Law, Performing Arts and Polytechnic. She has a number of national and international publications to her credit.

Dr. Deepak Langade MBBS, MD,PGDASS. He is professor and head in pharmacology at Dr.D.Y.Patil school of medicine Navi Mumbai. He has 20 year of professional experience in clinical Research ,Biostatistics, training and medical writing field. He is working on consultant to many pharmaceutical organization (merck,Novartis,MSD, Biocon, Dr.Reddy’s Ltd Piramal, Ranbaxy, Glenmark,etc). He is Faculty, Institute of Clinical Research India (ICRI), Mumbai. Also he has published 58 national & international publications in biomedical research . Also he is member of Maharashtra Research council (MRC), Directorate of medical Education and Research. Government of Maharashtra, Mumbai .

Prof. Rajendran R. B.Sc. (Hons) in Statistics and Mathematics MGM,LLB,FICWA,FICS He is completed his master degree in Finance management. He is fellow of charted ship broaking. He has 42 years experience in Shipping and 20 years teaching. He is Teaching Decision Making & Forecasting subject in JBIMS, Sydenham, Alkesh Dinesh Modi IES, MET, Atherva, MGM,IMU.

29

30

31

32

Entrance Test

Sample Question Paper: PGDASS and PGDAS

1. xyy ex then find dx

dy

(a) 2log1

log2

x

x

(b)

x

x

log1

log

(c) 2log1

log

x

x

(d)

2log1

1

x

2. If 1064 yxyx then find dx

dy

(a) x

y (b)

y

x

(c) xy (d) y

x

10

3. 74

27

2

3

3

x

xLimx

(a) 36 (b) 0 (c) 63 (d) Limit does not exist

4. 1

221

x

xxxLimx

(a) (b) 5

4 (c)

4

5 (d) 0

5. If xe exy then find dx

dy

(a) 11 xe xeex (b) xe ex (c) xe eex 1 (d) xexx log1

6. x

xLimx

51log

0

(a) e (b) 5 (c) (d) 2

7. 14

36

0

x

xx

xLim

33

(a) 0 (b) 2 (c) 1 (d) 2

1

8. If ,xxy find 2

2

dx

yd-

y

1

x

y

dx

dy

2

(a) 1 (b) 2 (c) 0 (d) 2

1

9. If 1X and 2X have independent Poisson distribution with parameters then X1+X2

is distributed as Poisson with parameters

(a) (b) 2 (c) 2 (d) 2

10. If X has exponential distribution with meanm

1then the

xXP

xXP

2

is equal to

(a) exp(-mx) (b) exp(-x) (c) exp mx (d) exp (mx)

11. Suppose X has binomial with mean 3 and variance 2,then

(a) P[X=0]<P[X=9] (b) P[X=0]=P[X=9] (c)P[X=0]>P[X=9] (d) P[X=0]=9P[X=9]

12. Match List I with List II and select the correct answer using the codes given

below the lists

List I List II A. Uniform distribution (0, 1) 1. Mean = Standard deviation

B. Exponential distribution 2. Mean= Variance

C. Binomial distribution 3. (Variance/Mean) is less than 1’

D. Poisson distribution 4.6(variance/mean) =1

(a) (A,1), (B,4), (C,3), (D,2)

(b) (A,4), (B,1), (C,3), (D,2)

(c) (A,1), (B,4), (C,2), (D,3)

(d) (A,4), (B,1), (C,2), (D,3)

13. Let Z be a random variate having standard normal distribution and

10,)( ZZP , then

(a) ZZ 1 (b) ZZ 1

(c) ZZ 11 (d) ZZ 21

14. If X is distributed as Normal with mean and variance 2 then E(X2) is equal to

(a) 2 (b) 22 (c) 2 (d) 2

34

15. Match list I with list II and select correct answer using the codes given below the

list

List I List II

A. Geometric 1. Tossing of coin

B. Poisson 2. Tossing a die

C. Binomial 3. Tossing of coin till head appears

D. Uniform 4. Telephone calls arriving at single booth

a) (A,3), (B,4), (C,2), (D,1)

b) (A,4), (B,3), (C,2), (D,1)

c) (A,3), (B,4), (C,1), (D,2)

d) (A,4), (B,3), (C,1), (D,2)

16. You are given 7.0BAP and .9.0BAP Determine P(A).

(a) 0.2 (b) 0.3 (c) 0.4 (d) 0.6

17.

x

t 21

1

dt is

a) x1tan1

b) x1tan

1

2

1

c) x1tan1

2

1

d) 2

1tan

1 1 x

18. isdxab

eb

a

tx

a)

abeet tatb

b)

abtee tatb

c) abtte

d)

te abt

19. Which of the following matrices has rank two?

a)

42

31 b)

11

11 c)

93

31 d)

42

21

20. A random sample of four policyholders is taken from a group of eight, comprising

three men and five women. If the random variable X denotes the number of male

policyholders in the sample then X can take values.

a) 4,3,2,1 b) 3,2,1,0 c) 4,3,2,1,0 d) 3,2,1

35

21.

0

4dxxe x is

a) 24 b) 6

1 c) 6 d)

24

1

22. IF A=

987

654

321

then r(A)=

a) three b) two c) one d) zero

23. In a statistical experiment of tossing four coins simultaneously, if a random

variable X represents number of heads appeared, then X has following

distribution

a) Geometric b) Binomial

2

1,16

c)Binomial

2

1,4 d) Hypergeometric

24. A box contains 100 items out of which 20 are defective. If 4 items are picked at

random from that box and X denotes number of defective items out of four then X

has following distribution

a) Binomial b) Poisson c) negative binomial d) Hypergeometric

25. Let X1 be b (2, p) and X2 be b (4,p). If 9

51Pr 1 X ,the 1Pr 2 X is

a)

4

4

31

b)

4

4

3

c) 1-

4

3

2

d)

4

3

2

26. Random variable X follows binomial distribution with parameters n and p. If for

the Binomial distribution E(X)=5 and Var(X)=4, then pair (n,p) is

a)

5

1,25 b)

5

4,25 c)

5

1,16 d)

5

4,16

27. dxexx2

2

1

2

2

1

a) -1 b) 1 c) 2

1 d)

2

1

36

28. Summary of observed values of random variable X is as follows 3 times –g, 5

times g, 2 times 0

Average value of X is a) .3g b) .5g c) -.2g d) .2g

29. A and B alternately toss a fair coin. The first one to throw a head wins. If A starts,

probability that A wins is

a) 2

1 b)

3

1 c)

3

2 d)

6

1

30. The probabilities of solving a problem by three students A, B and C are

respectively 8

3,

7

3 and

3

1. If all of them try independently, probability that the

problem will not be solved is

a) 21

5 b)

7

3 c)

3

2 d)

8

3

31. A small company paid each of its five clerks Rs. 22,000, each two stenos Rs.

50,000 each and the director Rs. 2,70,000 last year. The number of employees

earning less than mean salary is

a) 0 b) 4 c) 5 d) 7

32. If P[X=2] =1, then XVXE , is

a) (2,0) b) (2,2) c) (0,2) d) (2,1)

33. The mean and variance of -2,0,2 are respectively

a) (0,2) b) (2,8) c)

3

8,0 d) (-2,2)

34. If 1Q and 3Q are first and third quartiles then

a) 1Q median > 3Q b) 1Q < Median < 3Q

c) Median < 1Q < 3Q d) Median > 3Q >

1Q .

35. A student randomly guesses at the two questions on a true or false quiz. Let X=

number of correct guesses. The mean of X is.

a) 1 b) 2

1 c) 2 d) 0

37

36. Mean and standard deviation of (5,5) is

a) 5,5 b) 10,5 c) 5,0 d) 0,5

37. If A and B are two nxn square matrices then determinant of AxB is equal to

a) Det A x det B b) det A + det B c) n. det A d) n.det B.

38. If X follows normal distribution with mean zero and variance 2. Then max f(x) is

a) 2

1 b)

2

1 c)

2

1 d) 1

39. The distribution of marks of a large group of high school students is normally

distributed with 60 and 4 . The probability that a randomly selected

student has marks more than 60 is

a) .25 b) .05 c) .5 d) .80

40. If X follows N (5, ) which of the following is false?

a) Mean of X is five b) Median of X is five

c) Mode of X is five d) X is symmetric about zero

ANSWERS:

1. a 11. c 21. a 31. d

2. a 12. b 22. b 32. a

3. a 13. a 23. c 33. c

4. c 14. b 24. a 34. b

5. c 15. c 25. c 35. a

6. b 16. d 26. a 36. c

7. d 17. a 27. b 37. a

8. c 18. b 28. d 38. a

9. c 19. a 29. c 39. c

10. d 20. b 30. a 40. d

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