# Simulating normal random numbers in Python

Using the Box-Muller method

In my previous Medium story: https://oscarnieves100.medium.com/how-to-simulate-random-numbers-dad35905ecdb I discussed how to simulate random numbers in Python by using a little mathematical method known as “the inverse sampling theorem”. In it, I demonstrated how using nothing but uniformly distributed random numbers in the interval [0, 1] we could produce a set of random numbers from an exponential distribution, as shown in the Figure below:

I also discussed how this Inverse Sampling technique could also be applied to a variety of other probability distributions. However, it is essential to point out that this method only works if the cumulative distribution function of the desired random variable can be expressed in a closed-form, that is: in terms of elementary functions, and is also invertible.

In the case of normal random variables, the probability density function is given by

from which we can sample random numbers X ~ N(μ, σ²) — that is, normally distributed numbers with mean μ and variance σ². The cumulative distribution function associated with this is calculated by taking the probability…