Find a newly minted penny. Place it on its edge and spin it 20 times. Following Example...

Find a newly minted penny. Place it on its edge and spin it 20 times. Following Example E of Section 3.5.2, calculate and graph the posterior distribution. Spin another 20 times, and calculate and graph the posterior based on all 40 spins. What happens as you increase the number of spins?

Reference

Bayesian Inference A freshly minted coin has a certain probability of coming up heads if it is spun on its edge, but that probability is not necessarily equal to 1 2. Now suppose it is spun n times and comes up heads X times. What has been learned about the chance the coin comes up heads?We will go through a Bayesian treatment of this problem. Let , we might represent our state of knowledge by a uniform density on [0, 1]:

We will see how observing X changes our knowledge about , transforming the prior distribution into a “posterior” distribution.

Given a value θ, X follows a binomial distribution with n trials and probability of success θ: