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Convolution is a function-valued operation on two functions $f$ and $g$: $\int _{-\infty }^{\infty }f(\tau )g(t-\tau )d\tau$. Often used for obtaining the density of a sum of independent random variables. This tag should also be used for the inverse operation of deconvolution. DO NOT use this tag for convolutional neural networks.

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Problem with a factor in a convolution of two probability density functions

I wish to find the probability density function of the center of mass velocity, which is $v=\frac{v_1+v_2}{2}$ To obtain the pdf of $v$ I'm using the convolution formula $q(v)=\int^{\infty}_{-\infty … in account in the convolution formula, and provide a proper mathematical explanation. …
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