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Math Help - joint pdf probability

  1. #1
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    joint pdf probability

    suppose X and Y have the joint pdf
     <br />
f_{X, Y} = x + y, 0 < x, y < 1<br />
    Find P(X < 2Y)
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  2. #2
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    Quote Originally Posted by wik_chick88 View Post
    suppose X and Y have the joint pdf
     <br />
f_{X, Y} = x + y, 0 < x, y < 1<br />
    Find P(X < 2Y)
    \displaystyle \Pr(X < 2Y) = \int_{y=0}^{y = 1} \int_{x = 2y}^{x = 2} f(x, y) \, dx \, dy.
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  3. #3
    MHF Contributor matheagle's Avatar
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    Right, but X cannot exceed 1, with any probability, so the imposter must draw the line in the unit square.

    I'd switch the order of integration...

    1-\int_0^1\int_0^{x/2} (x+y)dydx
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  4. #4
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    Quote Originally Posted by matheagle View Post
    Right, but X cannot exceed 1, with any probability, so the imposter must draw the line in the unit square.

    I'd switch the order of integration...

    1-\int_0^1\int_0^{x/2} (x+y)dydx
    Right you are. I misread the support.
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  5. #5
    MHF Contributor matheagle's Avatar
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    thats why I'm the math beagle
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  6. #6
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    the final answer i got is \frac{19}{24} is this correct? thanks so much!
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