Time and Chance

The chapter opens with a comparison of a bar chart (or histogram) of the number of mRNA molecules seen at time = 2,000 seconds from the simulations of the preceding chapter to another bar chart of the heights of children in Victorian England. Despite the very different nature of these two types of data, the two histograms look remarkably similar. The text continues by discussing several meanings of the word “random” and contrasts randomness due to events at the quantum level to historical or population-level randomness. This second level of randomness substitutes a random model for an inaccessible history of the events in question. We next explore the idea of random variables: black boxes that produce random numbers following certain patterns like those of dice or coins. We examine the problem of flipping a coin a number of times and counting the heads, from which we derive the binomial distribution. We next explore random variables producing continuous outcomes by imagining a radiation “gun” that fires high-energy particles that can kill a cell. We work out that a distribution called the exponential distribution describes how long the cell will live under these conditions. We conclude by noting the existence of other continuous distributions such as the uniform and normal distributions.