Suppose we observe a sequence of i.i.d. random variables X1, . . . , X\". Their distribution is unknown, and has unknown mean it and known variance 02. In this question, we will investigate two different estimators for the mean u: the sample mean, and the socalled \"median of means\" estimator. In particular, we will analyze them in terms of how many samples n are required to estimate in to a given precision 15 and for a condence threshold 5. (d) (2 points) Fix a sample size no = [10 1. For each of the group means i, we define a binary random variable Zi: Zi = 1(15() - M/ Z E). In other words, Z; is 1 if the corresponding group mean is close to the true mean (within e), and 0 otherwise. Show that E[Zi]