Question: Q15, chapter 6, page 274 ,Introduction tp probability. Please solve this question: Let W = X 2 +Y 2 , with X, Y ( i.i.d.)

Q15, chapter 6, page 274 ,Introduction tp probability. Please solve this question:

Let W = X2+Y2, with X, Y ( i.i.d.) and N(0, 1). The MGF of X2 turns out to be (12t)1/2

for t < 1/2 (you can assume this).

(a) Find the MGF of W.

(b) What famous distribution that we have studied so far does W follow (be sure to

state the parameters in addition to the name)? In fact, the distribution of W is also a

special case of two more famous distributions!

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