Conditional Distribution Problem

aniguchisan

Hi all, given that I have the following distributions:

Which can be written as follows:

and

, where Xs ~ Negative binonmial (s,p)

Now, I am asked the following:

I don't quite know about how to tackle this problem. I know what a conditional distribution is, but don't know how to apply it here, so please guide me accordingly.

Finally, I am asked the following:

I sincerely request help for the above two questions. My concepts are a little weak here, so if I could be guided through the steps/answers for the above, I would be grateful. Thanks ever so much in advance.