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Let N be a positive integer random variable with PMF of the form pN(n)=1/2⋅n⋅2^(−n),n=1,2,…. Once we...

Let N be a positive integer random variable with PMF of the form

pN(n)=1/2⋅n⋅2^(−n),n=1,2,….

Once we see the numerical value of N, we then draw a random variable K whose (conditional) PMF is uniform on the set {1,2,…,2n}.

Find the marginal PMF pK(k) as a function of k. For simplicity, provide the answer only for the case when k is an even number. (The formula for when k is odd would be slightly different, and you do not need to provide it).

For k=2,4,6,…:

pK(k)=

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