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The counterpart for independent continuously distributed random variables with density functions <math>f, g</math> is
:<math>h(z)=(f*g)(z)=\int_{-\infty}^\infty f(z-t)g(t) dt = \int_{-\infty}^\infty f(t)g(z-t) dt</math>
The general formula for the joint pdf of X and Y is:
:<math>f_Z(z) = \int \limits_{-\infty}^{\infty} f_{XY}(x, z-x)~dx</math>
However, if X and Y are independent, then:
:<math>f_{XY}(x,y) = f_X(x) f_Y(y)</math>
and the general formula becomes the convolution of probability distributions:
:<math>f_Z(z) = \int \limits_{-\infty}^{\infty} f_{X}(x)~f_Y(z-x)~dx</math>
== Example derivation ==
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