# Linear combination, product and ratio of normal and logistic 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.