Question

As in the previous exercise, let È be the bias of a coin, i.e., the probability of Heads at each toss. We assume that È 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∣È=è]=nè.

a) Find the conditional mean squared error E[(K−E[K∣È=è])2∣È=è] if è=1/3.


b) Find the overall mean squared error of this estimation procedure.

Answer 1

a) = var(K/o)= np(1-p) = 9*(1/3)*(2/3)= 2

Answer 2

b) 3/2

Answer 3

b) integrate n*p*(1-p) , from 0 to 1