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$f(x,y) = {2\over 5}(2x+3y) \quad for\quad 0

and we want to know the distribution of $2X+3Y$

I did it in a very lousy way which is let $ U=2X+3Y ,\; V=X$

Then have $\;f_{U,V}(u,v)$ and then integer by V to get $\;f_U(u)$

So I tried $f_{U,V}(u,v) = f_{X,Y}(v,{u-2v\over 3})*{2\over5}={2u\over 15}$

$\int_0^\infty{2u\over 15}dv=$ then I think i might be wrong here....

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    Probably you mean that the joint density function of $X$ and $Y$ is $\frac{2}{5}(2x+3y)$ **in** the unit square, and $0$ elsewhere.2012-10-23
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    I think your approach is a good one, not lousy. :)2012-10-23

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