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On the product of triangular random variables. (English) Zbl 1195.33212

The probability density function (pdf) for the product of three independent and non-identical triangularly distributed random variables is derived by use of the Mellin transform and its inverse. It involves a consideration of various cases and subcases. The pdf for one subcase is obtained and the remaining cases are presented in tabular form.
The result is then applied to an electronic system consisting of n chips, where the numbers of defects in these chips are triangular random variables which are assumed to be independent. The total number of possible failures of the system will then be the product of n random variables.
Moreover, it is also indicated how to calculate the pdf for the product of n triangular random variables.

MSC:

33C90 Applications of hypergeometric functions
62E99 Statistical distribution theory
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