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Jensen's Inequality

  1. Feb 14, 2005 #1
    The variance can be written as Var[X]=E[X^2]-(E[X])^2. Use this form to prove that the Var[X] is always non-negative, i.e., show that E[X^2]>=(E[X])^2.
    Use Jensen's Inequality.

    Any sugestions? I just tried to prove that a function g(t) is continuous and twice differentiable, such that g''(t) > 0 which must imply it is convex.
    Then, I am stuck with the proof.
  2. jcsd
  3. Feb 14, 2005 #2


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    Science Advisor

    I am not sure how to use Jensen's inequality. However by using the relationship:

    E((X-E(X))2)=E(X2)-(E(X))2, the result is obvious.
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