Suppose that x and y are independent geometric random variables with the same parameter p.
(a) without any computations, what do you think is the value of p{x = i|x + y = n}? hint: imagine that you continually flip a coin hav- ing probability p of coming up heads. if the second head occurs on the nth flip, what is the probability mass function of the time of the first head?
(b) verify your conjecture in part (a).