Consider the multiple observation variant of Example 8.2:

Chapter , Problem 12

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Consider the multiple observation variant of Example 8.2: given that 8 = 8, the random variables Xl , ... , Xn are independent and uniformly distributed on the interval [0, 8], and the prior distribution of 8 is uniform on the interval [0, 1]. Assume that n > 3. (a) Find the LMS estimate of 8, given the values Xl , .. , xn of XI , ... , Xn . (b) Plot the conditional mean squared error of the MAP and LMS estimators, as functions of x = max{xI, ... , xn}, for the case n = 5. (c) If x is held fixed at x = 0.5, how do the MAP and the LMS estimates, and the corresponding conditional mean squared errors behave as n - oo?