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Let X1, X2 be i.i.d., and let X = 1 2 (X1 + X2) be the sample mean. In many statistics

Chapter 9, Problem 13

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QUESTION:

Let X1, X2 be i.i.d., and let X = 1 2 (X1 + X2) be the sample mean. In many statistics problems, it is useful or important to obtain a conditional expectation given X. As an example of this, find E(w1X1 +w2X2|X), where w1, w2 are constants with w1 +w2 = 1.

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QUESTION:

Let X1, X2 be i.i.d., and let X = 1 2 (X1 + X2) be the sample mean. In many statistics problems, it is useful or important to obtain a conditional expectation given X. As an example of this, find E(w1X1 +w2X2|X), where w1, w2 are constants with w1 +w2 = 1.

ANSWER:

Step 1 of 4

By the symmetry, we have that

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