Convolution of probability distributions: Difference between revisions

Revision as of 10:21, 15 August 2022

Revision as of 22:00, 31 August 2022

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:<math>H(z)=\int_{-\infty}^\infty F(z-t)g(t) dt = \int_{-\infty}^\infty G(t)f(z-t) dt</math>

If we start with random variables <math>X</math> and <math>Y</math>, related by <math>Z = X + Y</math>, and withoutwith knowledgeno ofinformation theseabout randomtheir variablespossible being independentindependence, then:

:<math>f_Z(z) = \int \limits_{-\infty}^{\infty} f_{XY}(x, z-x)~dx</math>