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Math Help - Joint Probability Distribution + Expectations

  1. #1
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    Joint Probability Distribution + Expectations

    Joint Probability Distribution + Expectations-joint-prob.jpg

    I have this Joint Probability table: I need to figure out

    a) E[X] (given Y=30)
    b) E[Y] (given X=5)

    I have worked something out, I'm not certain it is correct though.

    For a) I did: (1 x .10) + (5 x .05) + (8 x .15) = 1.55

    and for b) : (14 x .17) + (22 x .15) + (30 x .05) + (40 x .02) + (65 x .01) = 7.91

    Can anyone tell me if I am moving along the right track?

    Thanks!
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  2. #2
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    Re: Joint Probability Distribution + Expectations

    Quote Originally Posted by Walowizard View Post
    Click image for larger version. 

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    a) E[X] (given Y=30)
    b) E[Y] (given X=5)

    I have worked something out, I'm not certain it is correct though.
    For a) I did: (1 x .10) + (5 x .05) + (8 x .15) = 1.55
    and for b) : (14 x .17) + (22 x .15) + (30 x .05) + (40 x .02) + (65 x .01) = 7.91
    I have not (will not) do the calculations.
    BUT the setups are correct in both parts.
    Thanks from Walowizard
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  3. #3
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    Re: Joint Probability Distribution + Expectations

    Sorry, I am having one last problem with this table.

    Again based on the table in my first post, I have a question that says:

    What is the variance of Y?

    I think I have to do it like this:

    Var(Y) = (Probability that Y=14)*(14 - mean)^2 + P(Y=22)*(22-mean)^2 +............. P(Y=65)*(65-mean)^2

    My problem is finding the Probability that Y = 14, 22, etc.... and the mean. I believe I have calculated the mean correctly though, I came up with 34.2

    If anyone can help me out it would be great
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  4. #4
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    Re: Joint Probability Distribution + Expectations

    Sorry once again for bumping this so soon, but I think I have solved it! Just want to make sure :P

    So for the Variance of Y, I did this:

    (.21)(14-34.2)^2 + (.23)(22-34.2)^2 + (.30)(30-34.2)^2 + (.15)(40-34.2)^2 + (.11)(65-34.2)^2 = 238.2

    Have I solved this correctly? (I am still unsure about the mean being 34.2)
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