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Thread: urgent help need mean variance

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    urgent help need mean variance




    Hi everybody,

    If a random variable X is distributed in [0,1], can we say E[x]>var[x]?

    If yes, can you please give me a reference which is stated that or can you please give me the proof?

    I would be really thankful if you can help

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    Re: urgent help need mean variance


    Note that for any real number x \in (0, 1), and n > m

    we have

    x^n < x^m

    Therefore we have

    X^n < X^m for any random variables with support (0, 1)

    and thus

    E[X^n] < E[X^m]

    In particular,

    E[X] > E[X^2] > E[X^2] - E[X]^2 = Var[X]

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