We demonstrate here the close links between some ideas in probability and the properties of the molecular speed distribution of Maxwell and Boltzmann. In the two-dimensional case we show how the exponential probability distribution can be used to arrive at the median speed with little effort. In the three-dimensional case we show how the mode, median, mean and root-mean-square of the speed can all be found by using some basic tools from probability. As a numerical illustration, we consider the molecular speed of argon. We include in that illustration some very brief R code to show how useful R can be in finding numerical properties of probability distributions.
I. A. W. Macdonald (Sat,) studied this question.