Introduction to Continuous Probability Distributions

In the previous lesson, we described our first attempt of fixing System.Random:

• Make every method static and thread-safe
• Draw a clear distinction between crypto-strength and pseudo-random methods

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Continuous Probability Distribution

Let’s start by taking a step back and asking what we want when we’re calling NextInt or NextDouble or whatever on a source of randomness. What we’re saying is: we have a source of random Ts for some type T, and the values produced will correspond to some probability distribution. We can express that very clearly in the C# type system:

public interface IDistribution<T>
{
  T Sample();
}

In this lesson, we are going to look at continuous probability distributions, which we will represent as IDistribution<double>. We’ll look at integer distributions and other possible values for type parameter T in the upcoming lessons.

Now that we have an interface, what’s the simplest possible implementation? We have a library that produces a uniform distribution of doubles over the interval $[0.0, 1.0)$, which is called the standard continuous uniform distribution.

Here, the notation $[x,y$ ...