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

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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, 0.07] if d = 3.

(c) Find the probability that rt ∈ (0, 0.07] if d = 5.

math Statistics-And-Probability

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Answer 1

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Solution - Let, 74-X2+12+ -- the a) Distribution of of is: Since X; WN(0,1), then mit uyuschi Square withid of qr(. Кі, у Xo, ☺ of d=5, then at 5 degule of freedom rt ~X(6) Plocrt 20:07}=0

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