Assume you have the random variable X with distribution Geom(p), and estimate p.
a. As E(X) = 1/p, the natural approach to evaluate p is to get the sample from X and then take reciprocal 1/X. Illustrate that this is not the unbiased estimator for p.
b. Assume you take n i.i.d. samples X1,...,Xn, and you consider Y be fraction of the samples that equal 1. Illustrate that Y is unbiased estimator for p.