1. (45 points) Let X ~ Binomial(n,p). We estimate p by the estimator P* = X + 1 2+n (a) Find the bias of p* and its mean square error. (b) Are there any values of p for which the mean square error of our estimator p is lower than the mean square error of the standard, unbiased estimator p for p? If so, what are the value(s) of p? If not, show that MSE(p) < MSE() for all values of p.