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Probability Density Function - Need Help

  1. May 20, 2005 #1
    Probability Density Function -- Need Help!!

    Hi,

    Can someone please check my work if i did the problem correctly? thanks in advance.

    Here is the problem:

    Find the PDF of W = X + Y when X and Y have the joint PDF fx,y (x,y) = 2 for 0<=x<=y<=1, and 0 otherwise.

    here is my solution:
    [tex]
    \int_{0}^{1} \int_{0}^{w-y} 2dxdy
    [/tex]

    I work through the integral and get fw (w) = 2w-1 for w>0, and 0 for w<0.
     
    Last edited: May 20, 2005
  2. jcsd
  3. May 20, 2005 #2

    mathman

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    Gold Member

    Your answer is obviously wrong. f(w) is <0 for w<1/2. Moreover, the integral should be 1 - yours is 0.
     
  4. May 20, 2005 #3
    ok, i did a little more thinking :tongue2: and this is what i got now...

    For region w>0, the region of integration is outside so CDF Fw (w) is 0

    For region 0<=w<=1, i used double integration, and i get w^2/2

    For region 1<=w<=2, i get 2w-1-w^2/2

    For region w>2, i get 1.

    So to find PDF, i take the derivative, and i get the following:

    fw(w) = w for 0<=w<=1
    fw(w) = 2-w for 1<=w<=2
    fw(w) = 0 otherwise.

    Please let me know if i did anything wrong.
     
  5. May 21, 2005 #4

    mathman

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    Before I looked at your latest post, I worked it out myself. I got the same result as you did.
     
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