- #1
jrk012
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Homework Statement
So, I know the pdf for independent random variables is found by using the convolution; the pdf is f[sub:X+Y](a) = ∫ f[sub:X](a-y)f[sub:Y](y)dy, but can I just use the density function for a function of a random variable instead; that is: f[sub:X+Y](x[u,v], y[u,v])(Jacobian Inverse(x[u,v], y[u,v])) and then integrate it? It seems much easier that way.
Homework Equations
f[sub:X+Y](a) = ∫ f[sub:X](a-y)f[sub:Y](y)dy
f[sub:X+Y](x[u,v], y[u,v])(Jacobian Inverse(x[u,v], y[u,v]))
Jacobian Determinant: (∂u/∂x)(∂v/∂y)-(∂u/∂y)(∂v/∂x)
The Attempt at a Solution
More of a question on coursework than homework or a specific problem. However when I find the density function when U=X+Y I get f(x[u-v], y[v])