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Joint pdf question

  1. Dec 16, 2004 #1
    so X and Y have joing pdf f X Y(x, y) = 1/2 for 0 < y < x < 2, and 0 otherwise.

    find P(0< Y < 2/5 | X = 3/4)

    first, I dont understand how to read the function. So the function is equal to 1/2 when 0 < y < x < 2. And it is equal 0 otherwise.

    So I need to find Probabilty Y is between 0 and 2/5, given that X = 3/4? is that what it is asking?

    I think this has to do with integration, but what am I integrating? It's a single integeral right? and what do I do w/ the X = 3/4 part?

    actually, I got it...so no need for that.

    but this one. so f X Y (x,y) = c(y + x)y for 0<x<1 and 0<y<1.

    I need to find c.

    So I found the marginals, and what do I do to find c? am I suppose to put it against something?
    Last edited: Dec 16, 2004
  2. jcsd
  3. Dec 17, 2004 #2
    The total probability may be equal 1, right?
  4. Dec 17, 2004 #3
    You don't need to find the marginals. The integral of the function from -infinity to infinity for both x and y (which is the same as the integral from 0 to 1 for both x and y in this case) equals 1, and you just solve for c.
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