Unbiased Estimator for Gamma Distribution Parameter

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Homework Statement



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

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

Homework Equations



N.A.

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!!
 

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