As in the previous exercise, let Θ be the bias of a coin, i. e., the probability of Heads at each toss. We assume that Θ is uniformly distributed on [0,1]. Let K be the number of Heads in 9 independent tosses. We have seen that the LMS estimate of K is E[K∣Θ=θ]=nθ.
a) Find the conditional mean squared error E[(K−E[K∣Θ=θ])²∣Θ=θ] if θ=1/3.
b) Find the overall mean squared error of this estimation procedure.