Say you observe 4 independent Bernoulli random variables with a probability of success 0.2. Label them x1, x2, x3, x4. Keep in mind that the sum of Bernoulli random variables has a Binomial distribution, i.e. P(x1 + x2 + x3 + x4 = k) = 4! 0.2*0.84-k, for k = 0,1,2, 3, 4. (4 – k)!k! (a) What is the mean squared error of the estimator x1 + x2 + x3 + x4 4 with respect to the population mean, 0.2?

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