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Conditional Var

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  • Conditional Var

    I had difficulty with a problem that asked to find: var(Y/X=1)

    It was a discrete distribution and had only one outcome that gave Y/X=1:

    ie
    X=1 Y=2 1/8
    X=1 Y=1 1/2
    X=1 Y=0 1/4
    X=2 Y=1 1/8

    etc

    Did I read the question wrong? Was I missing something?

  • #2
    Originally posted by Big Daddy
    I had difficulty with a problem that asked to find: var(Y/X=1)

    It was a discrete distribution and had only one outcome that gave Y/X=1:

    ie
    X=1 Y=2 1/8
    X=1 Y=1 1/2
    X=1 Y=0 1/4
    X=2 Y=1 1/8

    etc

    Did I read the question wrong? Was I missing something?
    That's a fairly simple question; I think you're reading it wrong.

    I believe they are asking you for the variance of X, given that Y = 1. I think you read the question as the variance of (Y divided by X) = 1.

    E[X|Y=1] = (.25/.875)(0) + (.5/.875)(1) + (.125/.875)(2) = 6/7 (or approx. 0.8571)

    var(X|Y=1) = [(6/7)-0]^2 * (.25/.875) + [(6/7)-1]^2 * (.5/.875) + [(6/7)-2]^2 * (.125/.875) = (72/343) + (4/343) + (64/343) = 140/343 = 20/49 (or approx. 0.4082)
    Last edited by AJSeagles3; September 29 2005, 11:27 AM.

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    • #3
      i too had this question and believe they made it clear that it was X/Y not given Y. then it would be var(Y=X) which ive never seen a question like that before. i put 1/4 but was not positive at all.

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      • #4
        Originally posted by discman00
        i too had this question and believe they made it clear that it was X/Y not given Y. then it would be var(Y=X) which ive never seen a question like that before. i put 1/4 but was not positive at all.
        In that case, the question would be worded one of the following ways...

        1. Find var(Y/X).
        2. Find var(Y/X|X=1).
        3. Find var(Y/X|(Y/X)=1).

        All of the above are solvable. The answer to the 3rd one would be 0, obviously, but I highly doubt that's what they were asking for.

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        • #5
          I personally believe there was a typo on the problem. It was written as follows
          Find Var ((Y/X)=1), without the brackets of course, but with the y directly on top of the x, and the equal sign in line with the line under y, it reduced much to the same meaning.

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