Central Limit Theorem - proof part 2

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In deriving that the expectation of the sample mean equals mu, I think it's also important to note that the reason you can move the expectation inside the sum isn't merely because it's a linear operator, but rather also because the probability of any given sample is always the same. In the more general case of non-uniform probabilities, you can't move the sums like that.

cjbatesify
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When standarzing why do you multiply N with X_bar, u, and variance?

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