Question

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.

By performing some fancy and very precise measurements on the structure of that particular coin, we determine that È=1/3. Find the LMS estimate of K based on È.

Answer 1

E[K|Θ=θ]=n*θ=9*1/3=3