# Unbiased estimator of a probability?

1. Apr 1, 2010

### zli034

Say, $$x_1{}$$... $$x_n_+_1{}$$ are iid Bernoulli random variables with parameter p.

I want an unbiased estimator for probability Pr($$\Sigma_{}$$ $$x_1_._._._n{}$$ > $$x_n_+_1{}$$ )

I have failed to establish E(1 - $$\Pi$$ $$x_i{}$$) is unbiased estimator for the probability.

Any hints? thanks.

Last edited: Apr 1, 2010
2. Apr 8, 2010

### EnumaElish

Note that (1) a sum of Bernoullis is Binomial, and (2) a Bernoulli is a special case of Binomial. So your probability becomes the probability of the difference between two Binomials, one with n trials and one with a single trial, being greater than zero, Bi(n) - Bi(1) > 0.

3. Apr 8, 2010