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Joint PDF

  1. Nov 26, 2007 #1
    Can anyone tell me how to find the joint PDF of two random variables? I can't seem to find an explanation anywhere. I'm trying to solve a problem but I'm not sure where to go with it:

    Y is an exponential random variable with parameter [tex]\lambda=4[/tex]. X is also an exponential random variable and independent of Y with [tex]\lambda=3[/tex].. Find the PDF [tex]f_W(w)[/tex], where [tex]W=X+Y[/tex].

    I know that I simply use:

    [tex]f_W(w) = \int\int (x+y) f_{X,Y}(x,y)dydx[/tex]

    The problem is that I don't know how to find their joint PDF. I know their PDF's separately:

    x\geq 0\\0, & otherwise\end{array}\right.[/tex]

    x\geq 0\\0, & otherwise\end{array}\right.[/tex]

    Would this help me in anyway? Please help.
  2. jcsd
  3. Nov 26, 2007 #2
    the joint density function is simply the product of the individual density functions
    see here under independence:
    in that article you also find the correct formula for the density of X+Y, what you have there seems to be the formula for E[X+Y] imho
  4. Nov 26, 2007 #3
    Yeah sorry I realized I made a mistake, and that link helped a lot. Thank you!
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