# Math

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

pN(n)=12⋅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} .
Write down an expression for the joint PMF pN,K(n,k) .

For n=1,2,… and k=1,2,…,2n :

Find the marginal PMF pK(k) as a function of k .

Let A be the event that K is even. Find P(A|N=n) and P(A) .

P(A∣N=n)=

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1. n+1=i have no idea

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2. Anyone?

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3. 3) P(A∣N=n)= 1/(2^n)
P(A) = 1

I'm not 100% sure that they are right

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4. Nope all are partially right or entirely wrong..

1) (1/2)^(n+2)

2) (1/2)^((k/2)+1)

3) 1/2 , 1/2

4) YES

You are welcome!

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