Question: Suppose X and U are independent standard normal random variables. The outcome vari able Y is generated according to Y : X3 + U (a)

Suppose X and U are independent standard normal random variables. The outcome vari able Y is generated according to Y : X3 + U (a) Find the best prediction function in (93) of Y given that X : 9: under the MSE criterion. (b) Find the best linear prediction function 3(a) of Y given that X = 3: under the MSE criterion. (hint: EX 2 EX3 2 0, EX2 2 1, and EX4 2 3.) (c) Graph the functions m (3:) and E (at) in the same graph. Do you expect the two functions to be close to each other? Explain

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