1. Lecture 2 Topics for today Possible problems in Quantitative Analysis Approach Variables and their types Some basic concepts relating probability Derivatives

2. 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

3. 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

5. 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

7. 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.

8. 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

9. 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

11. 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

13. 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

14. Summary Quantitative techniques not free from problems Probability Variables and their types Derivative