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Math Help - Proving an equality

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    Proving an equality

    How do i prove that E[R^2] is greater than or equal to (E[R])^2??
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  2. #2
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    Quote Originally Posted by Pink Lady View Post
    How do i prove that E[R^2] is greater than or equal to (E[R])^2??
    This is related to the variance: on one hand, we define {\rm Var}(R)=E[(R-E[R])^2], which is (obviously?) nonnegative. On the other hand, you should expand the above expression in order to show that {\rm Var}(R)=E[R^2]-E[R]^2. Since this is nonnegative, you must have E[R^2]-E[R]^2\geq 0, and this is it. So you need to justify why the first expression of {\rm Var}(R) is nonnegative, and why it equals the second one.

    (There would be another more advanced/general answer involving convexity (and Jensen inequality), but you don't need that. )
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