The Molecular Speed Distribution of Maxwell and Some Routine Probability

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.