Let X and Y be independent random variables, and X has the standard normal distribution. Let Z = X +Y. • (a) Find Cov(X, Z). • (b) Assuming Y be exponentially distributed with parameter 1/2 find Var[XZ] and Var[XY] • (c) Find E[X*(X² +Y2)/2]. Does the answer depend on the distribution of Y?

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Let X and Y be independent random variables, and X has the standard normal
distribution. Let Z = X +Y.
(a) Find Cov(X?, Z).
(b) Assuming Y be exponentially distributed with parameter 1/2 find
Var[X Z] and Var[XY]
(c) Find E[X*(X? +Y?)/2]. Does the answer depend on the distribution
of Y?
Transcribed Image Text:Let X and Y be independent random variables, and X has the standard normal distribution. Let Z = X +Y. (a) Find Cov(X?, Z). (b) Assuming Y be exponentially distributed with parameter 1/2 find Var[X Z] and Var[XY] (c) Find E[X*(X? +Y?)/2]. Does the answer depend on the distribution of Y?
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