6.5 Randomness

Many programming languages have functions that return pseudo-random numbers. The prefix ‘‘pseudo’’ is there because they are not truly random numbers but nevertheless do well on statistical measurements of how well-distributed the results are.

Given four possible events E₀, E₁, E₂, and E₃ with associated probabilities p₀, p₁, p₂, and p₃, how might we use random numbers to simulate these events happening?

Suppose

The probabilities add up to 1.0, as expected. In Python 3, the random() function returns a random real number r such that 0.0 ≤ r < 1.0. Based on the value of r we get, we determine that one of the E₀, E₁, E₂, and E₃ events occurred.

If you are not using Python, use whatever similar function is available in your programming language and environment.

The general scheme is to run the following steps in order:

• r < p₀ then we have observed E₀ and we stop. In the example...