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.

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