6 Let p1

6 Let P1 < P2 < P3 . be the prime numbers, i.e. natural numbers which are not the product of two smaller natural numbers (1 is not prime with this definition). For all i e N, let pF , and Xi be a random variable taking values on {O, 1, 2, .. such that P(XI k) (1 Assume (Xi)i are independent. Let M Find the p.m.f. of M. You 2 72/6 and that each natural number has a unique might need that k decomposition in terms of products of primes. 16 marks]