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Math Help - Expected Value

  1. #1
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    Expected Value



    I don't understand what the question is actually asking for. I've never seen the notation for what I'm being asked to find. Any help would be greatly appreciated.
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  2. #2
    Super Member Random Variable's Avatar
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    Perhaps it's asking for the expected value of X given that X>1.96. But I've never seen that notation either.
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  3. #3
    MHF Contributor
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    could it be some wierd notation for the identity function?

    That is:

    1(X>1.96)=\left\{\begin{array}{cc}0,&\mbox{ if }<br />
x\leq 1.96\\1, & \mbox{ if } x>1.96\end{array} \right.

    if so
    E \left( 1(X>1.96) \right) = P(X>1.96)

    You can recognize this as the 97.5 percentile of the distribution, so the answer would be 0.025
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  4. #4
    Moo
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    It's the indicator function : \bold 1_A(x)=\begin{cases} 1 \text{ if } x\in A \\ 0 \text{ otherwise}\end{cases}
    Why do you find it "weird" ?

    And while talking probabilities, if A is an event, \mathbb{E}[\bold 1_A]=\mathbb{P}(A)

    So it's as SpringFan25 wrote, I'm just confirming it (I've already used this notation tons of times )
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  5. #5
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    Thanks!
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