lecture 2 topics for today possible problems in quantitative analysis approach variables and their...
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Lecture 2
Topics for today
• Possible problems in Quantitative Analysis Approach
• Variables and their types
• Some basic concepts relating probability
• Derivatives
Possible Problems in the Quantitative Analysis Approach
Problems are not easily identified
Conflicting viewpoints-linear or non linear relationship
Beginning assumptions
Fitting the textbook models
Validity of data
Hard-to-understand mathematics and statistics
Variables and their Types
Ratio scale Two values of a variable say X1 and X2,
(i)X1/X2 (ii)(X1-X2) (iii) X1≤ X2 and vice versa are meaningful quantities. Most economic
variable are ratio scale.
Interval Scale
Satisfies last two properties. Distance b/w two time periods (2012-1990) is meaningful.
But 1990/2012 is senseless.
Ordinal Scale
Only it satisfies the third property of ratio scale. Grades, A,B,C,D. Upper, Middle, Lower.
Example: Indifference curve in Economics
Nominal Scale:
None of the feature of ratio scale. Gender, male, female, marital status, single, married,
divorced, unmarried simply denote categories
Probability
• A probability is a numerical statement about the chance that an event will occur.
• Two basic rules regarding the probability
• 1- The probability, p, of any event is greater than or equal to 0 and less than or
equal to 1. 0≤p≤1
A- 0 means that an event is never expected to occur
b- 1 means that an event is always to occur.
2- The sum of the simple probabilities for all possible outcomes of an activity must be
equal to 1.
Examples:
Quantity Demanded Number of days
0 40 p=40/200 (.20)
1 80 p=80/200 (.40)
2 50 p=(50/200) (.25)
3 20
4 10
Types of probability
Two different ways to determine the probability
• Objective p(event)= number of occurrence of the event /total number of events
• Examples: tossing of a fair coin- it is based on the previous logic.
• Subjective: logic and history are not appropriate. So subjectivity arises.
Examples
• What is the probability that floods will come?
• What is the probability that depression will come in an economy?
• Which party will win the coming election in Pakistan?
• For this opinion polls are conducted and then probabilities are found.
Mutually exclusive and collectively exhaustive events
Mutually exclusive events : If only one of the event can occur on any one trial.
Collectively exhaustive events: They are said to be mutually exhaustive if the list include all the possible outcomes i.e. A U B= S.
Not mutually exclusive
The occurrence of one event does not restrict the occurrence of the other event.
• Examples: Drawing a 5 and drawing a diamond from a deck of cards- it can be both
5 and diamond
Adding mutually exclusive events• We are interested in whether one event or second event will occur.
• When events are mutually exclusive the law of addition is simply as follows.
• P(event A or event B)= p(event A)+ p(event B)
• Drawing spade or drawing a club out of a deck card are mutually exclusive.
13/52+13/52=1/2
• Venn diagram
• Addition of not mutually exclusive events.
• P(A or B)= P(A)+P(B)-P(A and B)
• Venn diagram
• Examples:
• In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5
girls made an A grade. If a student is chosen at random from the class, what is the
probability of choosing a girl or a student with A Grade?
• P(girl or A)= P(girl)+ P(A)- P(girl and A)= 13/30+9/30-5/30=17/30
Some Basic Concepts in Mathematics
Derivatives • Definition
• Maxima
• Minima
Rules of Derivatives
1- Constant function rule
2- Power function rule
3- Sum difference rule
4- Product rule
5- Quotient rule
6- Chain rule
7- Inverse function rule
8- Partial Derivatives
Notation
Dependent variable Independent variable
Explained variable Explanatory variable
Predictand Predictor
Regressand Regressor
Response Stimulus
Endogenous Exogenous
Outcome Covariate
Controlled variable Control variable
LHS RHS
Summary
• Quantitative techniques not free from problems
• Probability
• Variables and their types
• Derivative
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