The Bernoulli trials process is one of the simplest, yet most important, of all random processes. It is an essential topic in any course in probability or mathematical statistics. The process consists of independent trials with two outcomes and with constant probabilities from trial to trial. Thus it is the mathematical abstraction of coin tossing. The process leads to several important probability distributions: the binomial, geometric, and negative binomial.
- The Binomial Distribution
- The Geometric Distribution
- The Negative Binomial Distribution
- The Multinomial Distribution
- The Simple Random Walk
- The Beta-Bernoulli Process
Bernoulli trials appear in many chapters in this project, further evidence of the importance of the model.
- The chapter on Finite Sampling Models includes a number of topics based on a sampling with replacement from a dichotomous population. This type of sampling produces Bernoulli trials.
- The chapter on Games of Chance discusses several games based on Bernoulli trials.
- Estimation of the success parameter is discussed in the chapters on Point Estimation and Set Estimation.
- Hypothesis tests of the success parameter are discussed in the chapter on Hypothesis Testing.
Sources and Resources
I didn't major in math; I majored in miracles.—Mike Huckabee, Republican candidate for President of the US, 2008.