7. (3 points) Say one wishes to predict the outcome of a coi…
7. (3 points) Say one wishes to predict the outcome of a coin-tossing experiment through the best estimate of the value of a Bernoulli random variable with parameter . Let this estimated value be . (1 point) Find . (1 point) What is the mean-square error of this estimate? Express the error in terms of the parameter . (1 point) For what value of does the error reach maximum? Why?