let x be a continuous random variable. we know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. we are interested in estimating the mean of x, which we denote by h. we will use 1.5 as a conservative value (upper bound) for the standard deviation of x. to estimate h, we take n i.i.d. samples x1,x2,...,xn, which all have the same distribution as x, and compute the sample mean