Unbiased estimator of a probability?

[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.

 

[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.

 

[zli034]

Thanks I haven't thought about this view point.