addition of two empiric probability density functions

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If I have two empiric probability density functions (i.e. I can generate n points then form a histogram then normalize it) what is their "sum", I think convolution but I'm not sure. If yes then how to get $P_c$ = $P_a$ + $P_b$ ? where $P_a$, $P_b$ and $P_c$ are empiric probability density functions and $P_a$, $P_b$ are given? Second part of the question: If I have Pc and Pa can I get Pb?