Assuming Xi is iid normally distributed with N(μ,σ2)
In summation notation, what is the difference between
1) E(¯X2) and
2)E(X¯2)
(should have the bar over the entire X2)
3)E(¯X)2
so basically the difference between the expected value of the sample mean squared (1), the expected value of the RV squared's sample mean (2)(not sure how to put #2 into words sorry), and the square of the expected value of the sample mean (3).
I know
(2) E(X¯2) = (1n)(∑ni=1X2i)
(3) E(¯X)2 = (1n2)(∑ni=1Xi)2
But I'm confused on what (1) would be? How is it different from (3)?
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