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Math Help - random variable related

  1. #1
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    random variable related

    1) Let X be a random variable that takes values μ−a, μ, and μ+a with probabilities p, 1 − 2p, and p respectively. Show
    Pr(|X − μ| >= a) = Var(X)/a^2

    2) For a discrete random variable X, show that m = E(X) minimizes E[(X − m)^2]
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  2. #2
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    Quote Originally Posted by ashimb9 View Post
    1) Let X be a random variable that takes values μ−a, μ, and μ+a with probabilities p, 1 − 2p, and p respectively. Show
    Pr(|X − μ| >= a) = Var(X)/a^2
    Since \ |x-\mu| \ge a[/tex] when x=\mu-a and x=\mu+a (assuming a>0)

     <br />
Pr(|x-\mu| \ge a)=2p<br />

    You should know how to calculate Var(X) to complete the demonstration.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Since \ |x-\mu| \ge a[/tex] when x=\mu-a and x=\mu+a (assuming a>0)

     <br />
Pr(|x-\mu| \ge a)=2p<br />

    You should know how to calculate Var(X) to complete the demonstration.

    RonL
    But how can it be assumed for certain that a>0 ?
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  4. #4
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    Quote Originally Posted by ashimb9 View Post
    But how can it be assumed for certain that a>0 ?
    If a<0, then it is always true that |x-\mu|>a since |x-\mu| is always positive.
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  5. #5
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    Quote Originally Posted by ashimb9 View Post
    But how can it be assumed for certain that a>0 ?
    You will probabbly find it as an extra condition somewhere, because the question makes little sense otherwise.

    RonL
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