Solve the following:

Let X1, X2, . . . ,Xn independent normal random variables With variance 1 and EXZ- = m, and let Y : X12 + X22 + - - - + X3. Show that the characteristic function of Y is (t) 1 6 m9 = X W (1 2mm p 1 2a ' Where 6 := 211/112. (We call the distribution of Y non-centered X2 distribution with parameters (n, 6).) (Hint: Use induction.)