Question: Let be a continuous random variable. We know that it takes values between and , but we do not know its distribution or its mean

Let be a continuous random variable. We know that it takes values between and , but we do not know its distribution or its mean and variance, although we know that its variance is at most . We are interested in estimating the mean of , which we denote by . To estimate , we take i.i.d. samples , which all have the same distribution as , and compute the sample mean

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