Question: A random variable is Y p Qe where e N(0,1), Q 21 , and e and Q are independent. It will be

A random variable is Y Æ

p Qe where e » N(0,1), Q » Â21

, and e and Q are independent. It will be helpful to know that E[e] Æ 0, E

£

e2¤

Æ 1, E

£

e3¤

Æ 0, E

£

e4¤

Æ 3, E[Q] Æ 1, and var [Q] Æ 2. Find

(a) E[Y ] .

(b) E

£

Y 2¤

.

(c) E

£

Y 3¤

.

(d) E

£

Y 4¤

.

(e) Compare these four moments with those of N(0, 1). What is the difference? (Be explicit.)

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