Distribution of the product of two random variables

Common card · No. 471943

A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product Z = X Y {\displaystyle Z=XY} is a product distribution. The product distribution is the PDF of a product of two random variables. This is not the same as the product of the PDFs of two random variables. The concepts are sometimes ambiguously termed as in "product of Gaussians".

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