This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: PROBABILITY THEORY Dr. V.R. Bencivenga Economic Statistics Economics 329 PROBABILITY THEORY — PART 2 Outline Probability rules (1) Addition rule, rule of complements (2) Conditional probability (3) Multiplication rule, statistical independence (4) Bayes rule Bivariate probabilities Counting rules Objectives: Derive the rules of probability Understand how to identify which rule(s) apply when computing probabilities of events in a variety of situations involving randomness. Practice lots of problems! PART 3 2 PROBABILITY THEORY PROBABILITY RULES 3 PROBABILITY THEORY Example #5 — Causes of recession A newspaper polls economists about the causes of the 20089 recession. The economists were asked about two possible causes, and they could name either or both. 80% identified the credit crunch that developed in the aftermath of the financial crisis. 60% identified the loss of housing and financial wealth due to the financial crisis. 50% identified both. What is the probability that a randomlychosen economist will not identify either of these causes? 4 PROBABILITY THEORY C = credit crunch W = loss of housing and financial wealth DeMorgan’s law: ) W C ( P ) W C ( P Rule of complements: ) W C ( P 1 ) W C ( P Addition rule: P(C W) = P(C) + P(W) – P(C W) W C W C DeMorgan’s law: ) W C ( P ) W C ( P Rule of complements: ) W C ( P 1 ) W C ( P 5 PROBABILITY THEORY C = credit crunch W = loss of housing and financial wealth DeMorgan’s law: ) W C ( P ) W C ( P Rule of complements: ) W C ( P 1 ) W C ( P Addition rule: P(C W) = P(C) + P(W) – P(C W) C W C W DeMorgan’s law: ) W C ( P ) W C ( P Rule of complements: ) W C ( P 1 ) W C ( P Addition rule: P(C W) = P(C) + P(W) – P(C W) 6 PROBABILITY THEORY (1) Addition rule Addition rule for two events A and B: ) B A ( P ) B ( P ) A ( P ) B A ( P Addition rule for mutually exclusive events : ) B ( P ) A ( P ) B A ( P The probability of the intersection is subtracted to correct for double counting — to make sure basic outcomes in the intersection are counted exactly once. The intersection of A and B is empty, and so its probability is zero! 7 PROBABILITY THEORY A and A are mutually exclusive and collectively exhaustive. ) A ( P ) A ( P ) A A ( P apply the addition rule for mutually exclusive events 1 ) A A ( P use the definition of collectively exhaustive Therefore … Rule of complements: ) A ( P 1 ) A ( P 8 PROBABILITY THEORY Example #5 — Causes of recession A newspaper polls economists about the causes of the 20089 recession. The economists were asked about three possible causes, and they could name none, any, or all....
View
Full
Document
This note was uploaded on 02/26/2012 for the course ECONOMICS 329 taught by Professor Bencivenga during the Spring '12 term at University of Texas.
 Spring '12
 BENCIVENGA
 Economics

Click to edit the document details