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Suppose we observe a sequence of i.i.d. random variables X1, . . . ,Xn. Their distribution is unknown, and has unknown mean ,u and known variance 02. In this question, we will investigate how many samples n are required to estimate ,u to a given precision e and for a condence threshold 6. In other words, we'll use X1, . . . ,Xn to compute an estimate ,6, = [3(X1, . . . ,Xn) for the mean a. We want to see what sample sizes 7; guarantees that lF'(|,ii ,u| 2 e) S 6. (a) (2 points) For parts (a)(c), we'll use the sample mean as our estimator. Let S = i "' Xi. Use Chebyshev's inequality to show that n = g samples are sufcient for i=1 |Sn a| g e with probability at least 1 6