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linear combination of random variables; logistic distribution; normal distribution; products of random variables; ratios of random variables
The distributions of linear combinations, products and ratios of random variables arise in many areas of engineering. In this note, the exact distributions of $\alpha X + \beta Y$, $\vert X Y \vert $ and $\vert X/Y \vert $ are derived when $X$ and $Y$ are independent normal and logistic random variables. The normal and logistic distributions have been two of the most popular models for measurement errors in engineering.
[2] Prudnikov A. P., Brychkov Y. A., Marichev O. I.: Integrals and Series (Volumes 1, 2 and 3). Gordon and Breach Science Publishers, Amsterdam 1986
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