# Unbiased Estimator for Gamma Distribution Parameter

1. Jun 2, 2010

### Legendre

1. The problem statement, all variables and given/known data

I need to show that c / (sample mean X) is unbiased for b, for some c.

Where {X} are iid Gamma (a,b).

2. Relevant equations

N.A.

3. The attempt at a solution

I know how to show that (sample mean X) / a is unbiased for 1/b :

1) E(sample mean X / a) = (1/a)(1/n)(sum of E(X)) by iid
2) Then since E(X) = a/b, sum of E(X) = an/b. And we get the result.

But I have no idea how to evaluate E(1/ (sample mean X))! Where do I start? Thanks!!