7-21. Suppose a random variable Z is N(0, 1). Rewrite (7.A.2) in terms of even powers of t.

(1) Verify that mZ(t) = 

∞

n=0 antn, where an = -0 if n is odd;

1 2n/2(n2

)! if n is even.

(2) Using (4.36), demonstrate that E(Zn) = μ



n

= -0 if n is odd;

n!

2n/2(n2

)! if n is even.