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# Lecture12 - ECO ECO 220Y Random Variables and Probability...

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ECO 220Y L 12 ECO 220Y Lecture 12 Random Variables and Probability Distributions Bi i t Di t ib ti Bivariate Distribution Migiwa Tanaka Reading 7.2 1

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O tli Outline Bivariate Distribution Joint Probability/Density of Bivariate Random Variable Definition: Covariance Law of Expectation, Covariance, and Variance. 2
E l (f 7 55) Example: (from 7.55) Canadian custom b b f Bottles of Liquor (Y) observes number of bottles of liquor and f Cartons of 0 1 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 bottles Either 0 or 1 bottles. Either 0 or 1. How can we express the distribution of these two variables X and Y? 3

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Distributions Uni variate Probability Distribution: assigns probability of each the possible values for a single random variable Example: Tossing a coin ten times, Prob(Number of heads) Prob(Number of success of sales calls) Bi variate (or Joint) Probability Distribution: assigns b bili f h ibl i f l f probability of each possible pair of values for two random variables Example: Prob(L=0, C=1) from previous example.
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