Statistics Set Theory Permutations & Combinations Probability Theory Distributions Discrete Systems Binomial Binomial Plot Hypergeometric Hypergeometric Plot Poisson Poisson Plot Continuous Systems Normal Normal Plot Uniform Uniform Plot Exponential Exponential Plot Reliability Least Squares Resources Bibliography
Binomial Distribution

The binomial distribution, also known as Bernoulli distribution, describes the random sampling processes that all outcomes are either yes or no (success/failure) without ambiguity. In addition, the probability will not change from one trial to another (independent). In this case, the number of total available samples remains the same throughout the sampling process. In other words, the total number of available samples is either infinity or the chosen sample are always placed back to the sampling pool before the next trial (Sampling with replacement).

Suppose that the probability of success in a single trial is in a random sampling process and the failure rate is , where . The binomial distribution with exactly successes in trials, where , has the following important properties. See plots of binomial distributions.

 Binomial Distribution Density Function Distribution Function Mean Variance Standard Deviation
Hypergeometric Distribution

The hypergeometric distribution describes the random sampling processes that once a sample has been chosen, it will NOT be placed back to the sampling pool (sampling without replacement). In this case, the number of total available samples will decrease by one after each trial.

Suppose there are successes and failures in a sampling pool with available samples (). The hypergeometric distribution with exactly successes in trials, where , has the following important properties. See plots of hypergeometric distributions.

 Hypergeometric Distribution Density Function Distribution Function Mean Variance Standard Deviation

where and .

Poisson Distribution

The Poisson distribution describes the random sampling process that the desired outcomes occur relatively infrequently but at a regular rate.

Suppose there are on average successes in a large number of trials (large sampling period). The Poisson distribution with exactly successes in the same sampling period has the following important properties. See plots of Poisson distributions.

 Poisson Distribution Density Function Distribution Function Mean Variance Standard Deviation

where .