# Lecture12 - ECO ECO 220Y Random Variables and Probability Distributions Bivariate Distribution Migiwa Tanaka Reading 7.2 1 Outline Bivariate

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ECO 220Y Lecture 12 Random Variables and Probability Distributions Bivariate Distribution Migiwa Tanaka Reading 7.2 1

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Outline ivariate istribution Bivariate Distribution Joint Probability/Density of Bivariate Random Variable Definition: Covariance Law of Expectation, Covariance, and Variance. 2
Example: (from 7.55) Canadian custom Bottles of Liquor (Y) observes number of bottles of liquor and Cartons of 01 cartons of cigarette over time. Cigarettes (X) 0 0.63 0.18 X= number of cigarette cartons. Either 0 or 1. 1 0.09 0.10 Y= number of liquor ottles Either 0 or 1 bottles. Either 0 or 1. ow can we express the distribution of these two variables X and Y? How can we express the distribution of these two variables X and Y? 3

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Distributions ni riate robability Distribution: assigns probability of Uni variate Probability Distribution: assigns probability of each the possible values for a single random variable xample: Example: Tossing a coin ten times, Prob(Number of heads) rob umber of success of sales calls) Prob(Number of success of sales calls) Bi variate (or Joint) Probability Distribution: assigns
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## This note was uploaded on 03/01/2011 for the course ECON 220 taught by Professor Tanaka during the Spring '11 term at University of Toronto- Toronto.

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Lecture12 - ECO ECO 220Y Random Variables and Probability Distributions Bivariate Distribution Migiwa Tanaka Reading 7.2 1 Outline Bivariate

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