Lecture 2Topics 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 . (i)X1/X2 (ii)(X1-X2) (iii) X1≤ X2 and vice versa are meaningful quantities. divorced.D.Variables and their Types Ratio scale Two values of a variable say X1 and X2. male. unmarried simply denote categories . A. Ordinal Scale Only it satisfies the third property of ratio scale. Most economic variable are ratio scale. Middle. Grades. Distance b/w two time periods (2012-1990) is meaningful. female.B. Example: Indifference curve in Economics Nominal Scale: None of the feature of ratio scale. Gender. marital status.C. married. single. Interval Scale Satisfies last two properties. Upper. Lower. But 1990/2012 is senseless. . The probability.25) 20 10 .20) 80 p=80/200 (. Examples: Quantity Demanded 0 1 2 3 4 Number of days 40 p=40/200 (. of any event is greater than or equal to 0 and less than or equal to 1. p.Probability • A probability is a numerical statement about the chance that an event will occur. 0≤p≤1 A.0 means that an event is never expected to occur b. • Two basic rules regarding the probability • 1.1 means that an event is always to occur.The sum of the simple probabilities for all possible outcomes of an activity must be equal to 1. 2.40) 50 p=(50/200) (. . it is based on the previous logic. 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. • Subjective: logic and history are not appropriate. . So subjectivity arises.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 can be both 5 and diamond . Not mutually exclusive The occurrence of one event does not restrict the occurrence of the other event. A U B= S. • Examples: Drawing a 5 and drawing a diamond from a deck of cards.e. Collectively exhaustive events: They are said to be mutually exhaustive if the list include all the possible outcomes i.Mutually exclusive and collectively exhaustive events Mutually exclusive events : If only one of the event can occur on any one trial. 13/52+13/52=1/2 • Venn diagram • Addition of not mutually exclusive events. what is the probability of choosing a girl or a student with A Grade? • P(girl or A)= P(girl)+ P(A). If a student is chosen at random from the class. • P(A or B)= P(A)+P(B)-P(A and B) • Venn diagram • Examples: • In a math class of 30 students. • 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. 17 are boys and 13 are girls.P(girl and A)= 13/30+9/30-5/30=17/30 .Adding mutually exclusive events • We are interested in whether one event or second event will occur. 4 boys and 5 girls made an A grade. • When events are mutually exclusive the law of addition is simply as follows. On a unit test. . Sum difference rule 4.Power function rule 3.Inverse function rule 8.Some Basic Concepts in Mathematics Derivatives • Definition • Maxima • Minima Rules of Derivatives 1.Quotient rule 6.Partial Derivatives .Chain rule 7.Product rule 5.Constant function rule 2. . Notation Dependent variable Explained variable Predictand Regressand Response Endogenous Outcome Controlled variable LHS Independent variable Explanatory variable Predictor Regressor Stimulus Exogenous Covariate Control variable RHS . Summary • Quantitative techniques not free from problems • Probability • Variables and their types • Derivative .