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Given independent continuous random variables <math>X \sim f_Y</math> and <math>Y \sim f_Y</math>, the probability density function of <math>Z = X + Y</math>, that is, <math>f_Z</math> can be written as the following convolution:
:<math>f_Z(z) = E[f_Y(z-x)] = \int_{-\infty}^\infty f_Y(z-x) f_X(x)\, dx</math>
or
:<math>f_Z(z) = E[f_X(z-y)] = \int_{-\infty}^\infty f_X(z-y) f_Y(y)\, dy</math>
== Example derivation ==
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