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Thread: two easy questions I can't figure out

  1. #1
    Junior Member
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    two easy questions I can't figure out

    1. Let X be a random variable such that $\displaystyle E(|x|)=0$. Show that $\displaystyle P(X=0)=1$

    2. Let X have mean 2 and variance 0. Show that $\displaystyle P(X=2)=1$.

    They're both pretty simple and intuitively obvious, but with no other description of the random variable I really have no idea what properties to even work with.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Try markov or if you rather call it chebyshev's $\displaystyle \ne$.

    For all $\displaystyle \epsilon>0$

    $\displaystyle P(|X|>\epsilon)\le {E|X|\over\epsilon}=0$.

    Same idea with the second, just use the second moment and write X-2 for my X.
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