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Consider the following on-line learning method to estimate the expected value of a real-valued random variable X. We begin with an initial estimate µ0, and then for t = 1, 2, . . . , • Obtain xt as an independent identical distribution (i.i.d) sample of X, and • Revise our estimate as µt ← (1 − αt)µt−1 + αtxt . αt is the learning rate at step t. Assume X is normally distributed with mean µ and variance σ 2 . If we choose αt = 1 t , then E[µt ] is
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