Let the dynamics X_i i = 1, 2,.....,d be independently and identically distributed as Z ~ N (1, 0).

One approach for modeling the short-term interest rate r_t at any time t is given by defining r_t = X²₁ + X²₂ + ....+ X²_d

_{a) Describe the distribution of the continuous random variable} r_t

_{b) Find the probability that} r_{t = (0, 0.02) if d = 3.}

_{c) Find the probability that} r_{t = (0, 0.02) if d = 7.}