The Beta-Binomial Experiment

 Timeline Beta Distribution graph Beta-Binomial Distribution graph

Description

In the beta-binomial experiment, a random probability $$P$$ has a beta distribution with left parameter $$a$$ and right parameter $$b$$. Then, $$n$$ Bernoulli trials with success probabiity $$P$$ are tossed. Random variable $$Y$$ is the number of heads, and has the beta-binomial distribution with parameters $$n$$, $$a$$, and $$b$$. The values of $$P$$ and $$Y$$ are recorded on each run, and the outcomes of the trials are shown in the timeline graph (red for success and green for failure). The probability density function of $$P$$ is shown in the first graph, and the probability density function of $$Y$$ is shown in the second graph and is given in the second table. On each run, the value of $$P$$ is shown in the first graph, and the empirical probability density function of $$Y$$ is shown in the seond graph and recorded in the second table. The parameters $$n$$, $$a$$, and $$b$$ can be varied with input controls.