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If $X,Y$ are two independent random variables with CDFs $F_X,F_Y$, their sum has CDF $F_X \star F_Y$ ($\star$ is the convolution product).

What can be said about the quantile function of $X+Y$ ? The quantile function should be the inverse of $F_X \star F_Y$. Can we express that using the CDFs, quantiles (or even densities) of $X$ and $Y$ ?

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  • $\begingroup$ Did you ever figure out what the quantile function would look like? $\endgroup$
    – HW.
    Commented Jan 12 at 12:35

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