Bond, James Bond, has been ordered by M to destroy a nuclear facility in North Korea. Let NV be the number of attempts he makes until he succeeds. Suppose / follows a so-called geometric distribution with probability mass function fN(n) = (1 -p)"-1p, ne {1, 2, 3, ... }. Meanwhile, Q is waiting for M to give him more money to start building his next gadget. Let T be the amount of time Q has to wait. In fact, T is dependent upon how quickly Bond can succeed in his North Korean mission. Specifically, conditional on N = n, TI(N = n) ~ Gamma(n, A) with fTIN (t n) = (n) f-1ed t>0. (a) Find E(T) and Var(T). [Hint: You can use the properties of the geometric distribution, E(N) = 1/p and Var(N) = (1 - p)/p2, as well as those of the gamma distribution, E(T N = n) = n/> and Var(T|N = n) = n/x2.] (b) Find fr(t), the marginal distribution of T. (c) Find P(T > t), i.e., the probability that Q has to wait for more than t units of time