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Let the dynamics Xi , i = 1, 2, . . . , d be independently...

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 1 + X2 2 + . . . + X2 d .

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

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

(c) Find the probability that rt ∈ (0, 0.02] if d = 7.

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