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

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 = X²₁ + X²₂ + . . . + X²_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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