In this example, we define a prior probability distribution for a parameter theta, which takes on values between 0 and 1. We then define a likelihood function for observing data x given theta. Using Bayes' rule, we can compute the posterior probability distribution for theta given the observed data x. We use the numpy and pandas libraries to perform the necessary computations, and the matplotlib library to visualize the results. In this example, we generate two sets of binary data using a binomial distribution, and compute the posterior distribution after observing each set of data. We then plot the posterior distributions to see how they change as we observe more data.