P(X=k) = p(1-p)^k-1
if p have a uniform prior distribution on [0,1], what is the posterior distritubion of p? and what is the posterior mean?
Thanks!!
The joint distribution of X and p is...
where 0<p<1 and x=1,2,3,...
In order to obtain f(p|X) you need the marginal of X.
NOW use the beta density http://en.wikipedia.org/wiki/Beta_distribution
where x=1,2,3,...
This is a telescoping series that does sum to one.
Now divide and you should have that conditional distribution.