All needed are in the picture above (i hope so)
The Attempt at a Solution
to me it is extremely difficult because it is so complicated with many notations. Also, I actually don't know how to read the question properly to answer it
Is E(beta) is the event where we get even number of elements Beta ? I hope i get this point right. Otherwise, i have no idea what E means here.
One more point i can say is that the given pmf is Geometric distribution. My problem is i do not know how to start the question
Please help me to clarify it and answer any part that you can. You don't have to answer all of them or be so specific but please give me as much explanation as possible until you think that you give me enough clues to proceed with the subsequent questions.