Question: 3. Let Y be a Bernoulli random variable with unknown mean a, i.e.= P(Y = 0] = 1 ,u and P(Y = l] = a.

3. Let Y be a Bernoulli random variable with unknown mean a, i.e.= P(Y = 0] = 1 ,u and P(Y = l] = a. Let an = (Y1 + ---+ Yn) be the sample mean of IID Y; that have the same distribution as Y. How large must a be to ensure that the root mean square error (RMSE) in approximating p: by [in is no larger than 0.01? Your nal answer should not depend on n

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