This exercise provides an example of a pair of random variab
Question and Solution
This exercise provides an example of a pair of random variables X and Y for which the conditional mean of Y given X depe
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This exercise provides an example of a pair of random variables X and Y for which the conditional mean of Y given X depends on X but corr(X, Y) = 0. Let X and Z be two independently distributed standard normal random variables, and let Y = X2 + Z. a. Show that E(Y 0 X) = X2 . b. Show that mY = 1. c. Show that E(XY) = 0. (Hint: Use the fact that the odd moments of a standard normal random variable are all zero.) d. Show that cov(X, Y) = 0 and thus corr(X, Y) = 0.
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