Mid Term due Jun 8, 2021 18:59 CDT

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For all problems on this page, use the following setup:

LetN be a positive integer random variable with PMF of the form pN(n)=1/2n2n,n=1,2,....

Once we see the numerical value ofN, we then draw a random variableKwhose (conditional) PMF is uniform on the set{1,2,...,2n}

Discrete PMFs

LetA be the event thatK is even. FindP(A|N=n) andP(A)

P(AN=n)=

P(A)=

Independence 2

Is the eventA independent ofN