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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 it to a given precision 45 and for a condence threshold 6. In other words, we'll use X1, . . . ,Xn to compute an estimate ,5), = i1(X1, . . . ,Xn) for the mean M- We want to see what sample sizes at guarantees that lP(| i1 ,u,| 2 e) S 6. (b) (3 points) Now assume that each X; is bounded between a and b. Use Hoeffding's inequality to compute the number of samples n sufficient for |Sn - u|