Estimation : Binomial Distribution
Suppose T is a random variable such that
P(T=k) = (k-1)C(r-1) * p^r * (1-p)^(k-r) (It is a negative binomial distribution.).
I am trying to find the expected value E(r/T) (which is equal to r * E(1/T))
By (k-1)C(r-1) I mean (k-1)!/[(r-1)!*(k-r)!].