Statistical decision theory

5. In a given region there are 4,000,000 households and an unknown proportion p of these have an automatic dishwasher. In 500 households chosen at random there are 47 dishwashers. If s is the true number of households in this region that have dishwashers and a is the estimate, assume that the loss is given by lt(a,s) = $0.00001(s-at)2 on the basis of the sample survey what is the best estimate a and what would perfect information be worth at this point. [Hint s = K p, K = 4,000,000, and p satises the Beta distribution with parameters (500, 47).]