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If $X$ is picked from a normalized probability distribution $f(x)$ and $Y$ from $g(x)$, then what is the distribution of $X+Y$ in terms of $f$ and $g$? And that of $XY$?

And is there some equation that determines in general the distribution of $Q(X,Y)$ for any given function $Q$?

X and Y are independent.

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Do you know anything about these distributions? If you know nothing, we can talk about the expected value (linearity of expectation) and variance, for example. – pedrosorio Nov 4 '12 at 13:30
Are you saying there is no general formula or method for computing the distribution of X+Y, when we know f and g? There must be some relationship? – fff Nov 4 '12 at 13:30
$X+Y$ has density $f * g$, where $*$ is the convolution. – Stefan Hansen Nov 4 '12 at 13:35
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...That is, IF X and Y are independent. – Did Nov 4 '12 at 13:37
@did: My mistake. – Stefan Hansen Nov 4 '12 at 13:39

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