#### Description

The random experiment is to toss a coin \(n\) times, where the probability of heads is \(p\). The probability of heads is modeled with a prior beta distribution, having left parameter \(a\) and right parameter \(b\). The prior probability density function and the true probability of heads are shown in blue in the graph on the right. On each run, the number of heads \(Y\) is recorded in the data table. On each run, the posterior beta probability density function, which has left parameter \(a + Y\) and right parameter \(b + n - Y\), is shown in red in graph on the right. Also, the Bayesian estimate of \(p\),
\[U = \frac{a + Y}{a + b + n}\]
is shown on the graph in red and recorded in the data table on each run. Finally, the second table gives the true bias and mean square error of \(U\), and on each run gives the empirical bias and mean square error, based on the all of the runs of the experiment to that point. The parameters \(n\), \(p\), \(a\), and \(b\) can be varied with input controls.