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3. Let (X1, X2, X3) be a random sample of size 3 from a normal distribution with mean 0 and variance 1. We wish to
3. Let (X1, X2, X3) be a random sample of size 3 from a normal distribution with mean 0 and variance 1. We wish to compare the performance of two estimators: 0 (X1 + X2 + X3)/3 and 02 (X1 + X2 + X3)/4. Consider the squared error loss (0,a) = (a - 0)2. (a) Evaluate the risk functions of , and 02. [4 marks] (b) A student reasoned as follows: The risk of @1 is larger than that of 2 for ()
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