Before starting, we need to import `numpy`

and `matplotlib`

, which we can do by running the following code:

import numpy as np import matplotlib.pyplot as plt% matplotlib inline

This example is similar to the one given in the 2015 book, *Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference*, written by Cameron Davidson-Pilon. However, in our case, this is adapted to a financial context and rewritten so that the mathematical concepts intuitively arise from the code.

### Note

**Note**: You can view the example at the following link: http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/.

Let's imagine that you have a security that can either pay $1 or, alternatively, nothing. The payoff depends on a two-step process. With a 50% probability, the payoff is random, with a 50% chance of getting $1 and a 50% chance of making nothing. The 50% chance of getting the dollar is the **true payoff probability** (**TPP**),...