The number of persons coming through a blood bank until the first person with type A blood is found is a random variable Y with a geometric distribution. If p denotes the probability that any one randomly selected person will possess type A blood, then E(Y ) = 1/p and V(Y ) = (1 - p)/p2.
a. Find a function of Y that is an unbiased estimator of V(Y ).
b. Suggest how to form a 2-standard-error bound on the error of estimation when Y is used to estimate 1/p.