Question: 3. Three dependent random variables. Let X, Y, and Z be three random variables which satisfy 1 3 Y=X Z 2 +4' Where Z |X

3. Three dependent random variables. Let X, Y, and Z be three random variables which satisfy 1 3 Y=X Z 2 +4' Where Z |X has a normal N (X , 1) distribution and where 1E(X) = 1 and Var(X) = 1. (a) (3 pts) Find ]E(Y|X = 51:) (b) (3 pts) What is 1130')? (c) (4 pts) Recall the variance decomposition formula Var(Y) = ]E(Var(Y|X)) + Var(]E(Y|X)). Use this formula to nd Var(Y)

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