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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


(which is equal to r * E(1/T))

By (k-1)C(r-1) I mean (k-1)!/[(r-1)!*(k-r)!].

Solution Preview

It is a well know theorem that the expectation operator E(X) has the following properties:

(a) if X ≥ 0, then E(X) ≥ 0,
(b) if a,b are real, then E(aX+bY)=aE(X)+bE(Y), ...

Solution Summary

The expected value is calculated.