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SYLLABUS & PROGRAMME STRUCTURE
Statistics (Honours)
(Choice Based Credit System)
(Effective from the Academic Session 2017-2018)
First Semester
MAHARAJA BIR BIKRAM UNIVERSITY AGARTALA, TRIPURA: 799004
1
PROGRAMME STRUCTURE
Structure of Proposed CBCS Syllabus BA/BSc/BCom Honours
Semester Core Course
(14)
Honours
Ability
Enhancement
Compulsory Course
(AECC) (2)
Skill
Enhancement
Course (SEC)
(2)
Discipline
Specific
Elective
(DSE) (4)
Generic Elective
(GE) (4)
1 C1
C2
AECC1:
Environmental
Science
GE1
(Paper-I of selected
subject other than
Hons subject)
2 C3
C4
AECC2 :
(English/MIL
(Communication)
GE2
(Paper-II of
selected subject
other than Hons
subject)
3 C5
C6
C7
SEC1 GE3
(Paper-III of
selected subject
other than Hons
subject)
4 C8
C9
C10
SEC2 GE4
(Paper-IV of
selected subject
other than Hons
subject)
5 C11
C12
DSE1
DSE2
6 C13
C14
DSE3
DSE4
2
First Semester
Core Course - Paper- I
Descriptive Statistics & Basic Concepts of Probability
TOTAL MARKS – 100
(Theory – 70, Practical-30)
Unit I (Statistical Methods)
Introduction to Statistics: Definition, scope and Limitations of statistics, Use of statistics.
Collection and classification of data: Primary data and secondary data, methods of collection
of data, Scrutiny of data. Classification, principles of classification, types of classification.
Tabular presentations of data. Diagrammatic representation of data. Frequency
distribution and its constructions. Graphical presentations of frequency distribution.
Unit II (Central tendency, Dispersion & Moments)
Concept of central tendency, Different measures of central tendencies. Empirical
relationships between different measures. Concept of dispersion, Different measures of
dispersion and their properties. Different types of moments, relationships between raw and
central moments. Sheppard's corrections for moments (without proof). Skewness and
Kurtosis and their measures. Boxplot.
Unit III (Bivariate Correlation & Regression)
Bivariate data, Scatter diagram, Correlation coefficient and its properties. Rank correlation-
Spearman's & Kendall's measures.
Principle of Least squares. Concept of regressions, Regression lines, Important results
relating to regression lines. Fitting of Polynomial, Inverse, Exponential and Growth curve.
Unit IV (Probability)
Random experiment, Sample point, Sample space, different types of Events, Meaning of
Probability, Classical, Statistical and Axiomatic definitions of Probability. Limitation of
classical definition of Probability, Theorem on the Probability of union of Events.
Conditional Probability, Theorem on conditional Probability, Statistical independence of
Events, Bayes' theorem and its application.
Practical
List of Practical (Computational tools: Electronic Calculator & Spreadsheet Softwares)
1. Graphical representation of non-frequency data (Bar-Diagram, Line-Diagram, Pie
chart, Stem-and-leaf plot, Pictograms).
2. Construction of frequency distribution (Grouped & Ungrouped).
3. Graphical representation of frequency data (Histogram, Frequency polygon, Ogives,
Boxplots).
3
4. Summary statistics (Raw, Grouped & Ungrouped data).
5. Pearson’s correlation coefficient & Linear regression.
6. Spearman's rank correlation coefficient.
7. Kendall's correlation coefficient.
8. Curve fitting by least square method: Linear, Polynomial, Inverse, Exponential and
Growth curve.
9. Random Experiments & Computation of Probabilities for different Events.
Suggested Reading
1. Goon A.M., Gupta M.K. & Dasgupta B. (2002): Fundamentals of Statistics (Vol-I),
World Press, Kolkata.
2. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory
(Vol-I), World Press, Kolkata.
3. Rohatgi V.K. (1984): An Introduction to Probability Theory & Mathematical
Statistics, John Wiley.
4. Kendall M.G. & Stuart A. (1966): Advanced Theory of Statistics (Vol-I & II).
5. Gupta S. C., Kapoor V. K.: Fundamentals of Mathematical Statistics, Sultan Chand &
Sons.
4
First Semester
Core Course - Paper- II
Essential Mathematics for Statistics
TOTAL MARKS – 100
(Theory – 70, Practical-30)
Unit I (Elementary Mathematics)
Permutation & combination, Arithmetic & Geometric Progression. Binomial expansion for
positive & negative indices. Series Expansions of Exponential and Logarithmic Functions.
The principle of mathematical induction.
Unit II (Calculus & Mathematical Analysis)
Limit, Continuity and Differentiability of functions. Total & Partial Differentiation.
Maximum and Minimum of univariate & bivariate functions. Integration of univariate &
bivariate functions. Beta & Gamma Integration.
Convergence of sequence and series, Absolute convergence, Simple tests of
convergence (root test and ratio test), Basic concepts of Pointwise convergence and Uniform
convergence.
Unit III (Vector & Matrix Algebra)
Basic concept on Vector space with real field, Linear dependence of vector, Basis and
dimension of a vector space., Orthogonal vectors.
Definition of a Matrix, Different types of matrix, Matrix operations, Elementary
matrices and their uses, Rank of a matrix, Inverse of a matrix, Determinants, Quadratic
forms, Reduction of Quadratic form to canonical form. Basic concept of Characteristic roots
and vectors.
Unit IV (Numerical Analysis)
Interpolation: Difference operators (, E, D), Polynomial approximation, Difference table,
Newton's forward and backward interpolation formulae, Lagrange's interpolation formula.
Numerical Integration: Trapezoidal & Simpson's one-third rules. Euler maclaurin
summation formula.
Numerical solutions of univariate equation: Bisection, Iteration & Newton-Raphson
methods. Convergences of Iteration and Newton-Raphson methods.
Stirling’s approximation to n! for large n.
5
Practical
List of Practical (Computational tools: Electronic Calculator & Spreadsheet Softwares)
1. Interpolation by Newton's forward, Newton's backward & Lagrange's interpolation
formulae.
2. Numerical Integration by Trapezoidal & Simpson's one-third rules.
3. Numerical solutions of univariate equations by Bisection, Iteration & Newton-
Raphson methods.
4. Determinant of Matrix by Pivotal condensation method.
5. Inversion of Matrix by Gauss-Jordan method.
6. Solution of linear equations by Gauss elimination & Gauss Jordan methods.
7. Computation of Characteristic roots and vectors.
Suggested Reading
1. Kalyan K. Mukherjee: Numerical Analysis, New Central Book Agency (P) Ltd,
Kolkata.
2. Goon A.M., Gupta M.K. & Dasgupta B. (1994): An Outline of Statistical Theory
(Vol-I), World Press, Kolkata.
3. Sastry S.S(1987): Introductory Methods of Numerical Analysis, Prentice Hall..
4. Jain, Iyengar, Jain: Numerical Methods, New Age International Publishers.
5. J.B. Scarborough: Numerical Mathematical Analysis, Oxford and IBH.
6. S. C. Malik, Savita Arora: Mathematical Analysis, New Age International Publishers.
7. A. M. Goon: Vectors & Matrices, World Press, Kolkata.
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