Example class 11

# Example class 11 - The University of Hong Kong Department...

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The University of Hong Kong Department of Statistics and Actuarial Science STAT1301 Probability and Statistics I Example class 11 Conditional Expectation & Review Review I. Conditional Expectation Suppose X and Y are discrete random variables and the conditional frequency function of Y given x is . The conditional expectation of Y given X=x is For continuous random variables, II. The Law of Total Expectation III. Exercise 1. Consider X and Y be random variables having a joint density function given by a) Verify that f is a joint density function b) Determine their marginal density functions c) Calculate the covariance between X and Y. Are X and Y independent? d) Determine the conditional densities, and , of X given Y=y and of Y given X=x respectively e) Calculate E[Y|X=x] and Var(Y|X=x) for X>0 f) Show that the unconditional distribution of X is exponential of rate 2. g) Deduce from above the unconditional expectation and variance of Y. 2.

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## This note was uploaded on 04/29/2010 for the course STAT 1301 taught by Professor Smslee during the Spring '08 term at HKU.

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Example class 11 - The University of Hong Kong Department...

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