Let Y = X + for some numbers , R. Compute l1 = E [(Y E[Y |X])2]. [3] Again,

1: let X be a random variable with finite variance. Additionally, let A U(1,1) such that X and A are independent and consider Y = AX. You may use without proof that A*2 X*2. compute l1= E [(Y E[Y |X])*2]

2:Compute l2 = E [(Y E[Y |X])*2] expressing your final result in terms of E[X*k] for some value or values of k that you should specify.

3:Provide an interpretation of the quantities l1 and l2 obtained in parts (a) and (b) above in terms of the ability to predict Y given the value of X and explain any difference you observe