Suppose that X has a standard normal distribution. Let the
Chapter 5, Problem 57E(choose chapter or problem)
Suppose that X has a standard normal distribution. Let the conditional distribution of Y given X = x be normally distributed with mean \(E(Y \mid x)=2 x\) and variance \(V(Y \mid x)=2 x\).
Determine the following.
(a) Are X and Y independent?
(b) \(P(Y<3 \mid X=3)\)
(c) \(E(Y \mid X=3)\)
(d) \(f_{X Y}(x, y)\)
(e) Recognize the distribution \(f_{X Y}(x, y)\) and identify the mean and variance of Y and the correlation between X and Y .
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