Timeline Distribution graph Distribution graph

#### Description

In this experiment, a random probability $$P$$ has a beta distribution with left shape parameter $$a$$ and right shape 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 top graph shows the sequence of Bernoulli trials in a timeline, with each success as a red dot and each failure as a green dot. The first distribution graph shows the probability density function and empirical probability density function of $$P$$. The second distribution graph shows the probability density function and empirical probability density function of $$V$$. The first table records the outome $$(P, V)$$ of the experiment. The second table records the same information in text form as the graph above it. The parameters $$k$$, $$a$$, and $$b$$ can be varied with input controls.