Let Xi > 0 be the time-to-first fracture after treatment initiation (measured in months) for the ith subject, where i = 1, 2, ..., n. We model the fracture times as X1, X2, . .., Xn ~ Exp(0). Here, X ~ Exp(0) denotes the exponential distribution with scale 0 > 0 having density f(x) = ze " for x > 0 and f(x) = 0 elsewhere. You must use this parameterization for the problem. For some fixed constant T > 0, let v, = P(X > T). Ideally, the probability will be high - indicating that osteoporosis patients on the new BP drug will remain fracture free for at least 7 months with high probability. a. Integrate the given density to find an expression for v, in terms of 0 and T. b. Find the MLE of 0, denoted 0. Verify it is a max. Find the asymptotic distribution of Vn(0 - 0) A