X1and X2 are independently distributed random variables with

P(X1 = Z+1 ) = P(X1 = Z-1 ) = 1/2

P(X2 = Z-2 ) = P(X2 = Z+2 ) = 1/2.

Find the value of a and b which minimize the variance of Y = aX1 + bX2 subject to the condition that E[Y] = Z.

What is the minimum value of this variance?