Beta-Negative Binomial Experiment

Description

In this experiment, a random probability \( P \) has a beta distribution with left parameter \( a \) and right parameter \( b \). Then, Bernoulli trials with success probabiity \( P \) are performed. Random variable \( V \) is the trial number of the \( k \)th success, and has the beta-negative binomial distribution with parameters \( k \), \( a \), and \( b \). The timeline graph in the middle shows the sequence of Bernoulli trials, with each success as a red dot and each failure as a green dot. Variables \(P\) and \(Y\) are recorded in the data table. The distribution of \(P\) is described in the top graph, and the distribution of \(Y\) is described in the second distribution graph and the distribution table. The parameters \( k \), \( a \), and \( b \) can be varied with input controls.