Suppose there are N cable cars in San Francisco, numbered sequentially 1 to N. You see
a cable car at random; it is numbered x. You wish to estimate N. Assume your prior
distribution on N is the Geometric-distribution with success probability parameter p.
(a) What is the expectation of the prior distribution for N? (1/p)
(b) What is your posterior distribution for N? Simply state the involved normalizing constant as an unevaluated sum.
I'm have problems with part (b) - I'm guessing it has to depend on x somehow (since N cannot be smaller than x), but i'm not sure if throwing in a characteristic function would do it.