Question: 4. Let the dynamics Xi , i = 1, 2, . . . , d be independently and identically distributed as Z N(0, 1). One

4. Let the dynamics Xi , i = 1, 2, . . . , d be independently and identically distributed as Z N(0, 1). One approach for modeling the short-term interest rate rt at any time t is given by defining rt = X2 + X2 + . . . + X2 .

1 2 d

(a) Describe the distribution of the continuous random variable rt.

(b) Find the probability that rt (0, 0.02] if d = 3.

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