3. The continuous random variables X and Y have known joint probability density function fxy(x, y) given by fxy(x, y) = [2e-(x+y) 0 x≥0, y≥0, x≤y otherwise a) Obtain the conditional probability density function fx(x/Y = y) of the random variable X. b) Obtain the conditional probability density function f(y/X=x) of the random variable Y. c) Verify that the density functions of a) and b) are valid (non negative and integrate to 1.) d) Obtain the expected values E{X/Y = y} and E{Y/X=x}.

3. The continuous random variables X and Y have known joint probability density function fxy(x, y) given by fxy(x, y) = [2e-(x+y) 0 x≥0, y≥0, x≤y otherwise a) Obtain the conditional probability density function fx(x/Y = y) of the random variable X. b) Obtain the conditional probability density function f(y/X=x) of the random variable Y. c) Verify that the density functions of a) and b) are valid (non negative and integrate to 1.) d) Obtain the expected values E{X/Y = y} and E{Y/X=x}.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 23E

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