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Math Help - X and Y joint pdf probability question

  1. #1
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    X and Y joint pdf probability question

    If X and Y have the joint pdf
    f_{X,Y}(x,y) = 2, \ \ \ 0 < x < y < 1,
    then find P (0 < X < 0.5 | y = 0.75)
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  2. #2
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    Quote Originally Posted by wik_chick88 View Post
    If X and Y have the joint pdf
    f_{X,Y}(x,y) = 2, \ \ \ 0 < x < y < 1,
    then find P (0 < X < 0.5 | y = 0.75)
    What thoughts have you had? Where are you stuck?
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  3. #3
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    i havent ever done a joint pdf question where the probability has the "given y = ..." in it!
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  4. #4
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    Quote Originally Posted by wik_chick88 View Post
    i havent ever done a joint pdf question where the probability has the "given y = ..." in it!
    In the first instance, I suggest you refer to your class notes or textbook for the definition of the conditional density of X given Y = y ....

    After doing so, please ask for more help if required.
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  5. #5
    MHF Contributor matheagle's Avatar
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    find the conditional density of X given Y
    First you must find the marginal of Y and divide the joint density by that marginal
    When you finally have the conditional density, plug in your value for y and integrate x over the region.
    HOWEVER, since the joint density is uniform over the triangle it will be uniform over the line y=.75
    since you want 0<x<.5 the answer should be 2/3 which is two-thirds of that line.
    DRAW the region and you will see how obvious this is.
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