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Math Help - Probability: Sums and Products of Random Variables

  1. #1
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    Probability: Sums and Products of Random Variables

    Suppose that X is uniformly distributed on (0,2), Y is uniformly distributed on (0,3), and X and Y are independent. Determine the distribution functions for the following random variables:

    a)X-Y
    b)XY
    c)X/Y

    3. The attempt at a solution

    ok so we know the density fx=1/2 and fy=1/3. Since they are independent then fxy(xy)=(1/2)*1/3)=1/6. So we will integrate 1/6 over the rectangle with y (height) 3 and x (width) 2. for a) we have P(X-Y<=Z) = P(X-Z<=Y). This is were I get stuck. I am not sure what my limits of integration are. I know that X-Y can be no less than -3 (0-3). and no more than 2 (2-0). How do I go about finding the limits of integration? Same thing with b and c. For example b yield P(XY<=Z) which is equal to P(Z/X<=Y). So that would be the area of the rectangle under the hyperbola Z/X.
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  2. #2
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    Hi,
    I haven't looked at this stuff for decades but instead of looking for P(X-Y<=Z) shouldn't you be trying to find P(x-y = k)???.
    Steven
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  3. #3
    Moo
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    Quote Originally Posted by mathprofessor View Post
    Hi,
    I haven't looked at this stuff for decades but instead of looking for P(X-Y<=Z) shouldn't you be trying to find P(x-y = k)???.
    Steven
    Easy, it's 0.
    They're uniform continuous distributions !
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  4. #4
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    yeah, yeah, you got me. good job!
    Steven
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