Distributions
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General Terms

The general terms of probability are given in the Probability Theory section. They are also summarized in the following table:

TermDiscrete SystemContinuous System
Density Function F(x)
Distribution Function F(x)
Mean mu
Variance sigma^2
Standard Deviation sigma

Common Distributions in Discrete Systems

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). See plots of binomial distributions.

Hypergeometric Distribution: The hypergeometric distribution describes the random sampling processes in which once a sample has been chosen, it will NOT be placed back into the sampling pool (sampling without replacement). In this case, the number of total available samples will decrease by one after each trial. See plots of hypergeometric distributions.

Poisson Distribution: The Poisson distribution describes the random sampling process in which the desired outcomes occur relatively infrequently but at a regular rate. See plots of Poisson distributions.

For further summaries and plots, see the Distributions in Discrete Systems section.

Common Distributions in Continuous Systems

Normal Distribution: The normal distribution, or Gaussian distribution, is a symmetrical distribution commonly referred to as the bell curve. It can be considered as a special case of the binomial distribution with a very large number of trials and an equal success/failure rate. See plots of normal distributions.

Uniform Distribution: The uniform distribution has a constant success rate on a certain intervals and a zero success rate on the others. See plots of uniform distributions.

Exponential Distribution: The Exponential distribution arises in the treatment of reliability calculations. It is similar to the Poisson distribution without successful cases and the probability of desired outcomes diminishes as the trial number increases. See plots of exponential distributions.

For further summaries and plots, please see the Distributions in Continuous Systems section.

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