8. (1D points): Let X he a binomial random variable with parameters p E (D, 1) and n = I], 1, 2, . . .. In other words, for k = [1,11 2, . . . , n, n! 1P{X = kl = mpkll Pl_k- If n 1' oo and p l, U' such that up > A, show that the distribution of the random variable X converges to that of a Poisson random variable with mean A. For simple derivations, you can assume that up = A all the time as n > 00. Note: This is often called 'the law of small numbers1 and the basis for the socalled 'Poisson limit' as discussed in class with several examples