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:(adsbygoogle = window.adsbygoogle || []).push({});

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:

[tex]f_X(x)=\left\{\begin{array}{cc}3e^{-3x},&

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

[tex]f_Y(y)=\left\{\begin{array}{cc}4e^{-4x},&

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

Would this help me in anyway? Please help.

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# Joint PDF

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