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Thread: demonstration with discrete random variable

  1. #1
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    demonstration with discrete random variable

    I would like to know if anybody from this forum have some insights about how to handle this demonstration:

    "Show that for any discrete random variable X, etE[X] <= E[etX], where t is fixed and belongs to R." (E is expected value)

    Maybe this is related with Jansen inequality, but certainly I'm not good regarding demonstrations.

    By the way how can I learn the way of posting formulas in the forum?

    Regards.
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  2. #2
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    Re: demonstration with discrete random variable

    Quote Originally Posted by rbriceno View Post
    I would like to know if anybody from this forum have some insights about how to handle this demonstration:
    "Show that for any discrete random variable X, etE[X] <= E[etX], where t is fixed and belongs to R." (E is expected value)
    Maybe this is related with Jansen inequality, but certainly I'm not good regarding demonstrations.
    By the way how can I learn the way of posting formulas in the forum?
    You must learn to code in LaTeX.

    \$e^{\mathcal{E}[tX]}\$ gives $e^{\mathcal{E}[tX]}$

    \${\mathcal{E}[e^{tX}]}\$ gives $\mathcal{E}[e^{tX}]$
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  3. #3
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    Re: demonstration with discrete random variable

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