Suppose f(x) symmetric. Prove E[|x|]^2 <= variance(x) = E[x^2]-E[x]^2.
Attempt:
E[|x|]^2 +E[x]^2 <= E[|x|]^2 +E[|x|]^2 = 2E[|x|]^2 (?) <= E[x^2]
I do not know how to show 2E[|x|]^2 <= E[x^2].
Last edited by stephanie; 01-24-2014 at 12:44 PM.
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