Question: 6 Let p1 6 Let P1 < P2 < P3 . be the prime numbers, i.e. natural numbers which are not the product of two

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

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]

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