The Common Discrete Probability Functions

This is a companion Web site to

P-values for the Popular Distributions

The following JavaScript compute the probability mass function (p) and cumulative distribution function (F) for the the widely used discrete random variable.

**Discrete Random Variables:** A discrete random variable is used to model a random outcome with a finite or countable number of possible outcomes. That is, a discrete random variable is one that may take on only a countable number of distinct values. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples are the number of patients in a doctor's surgery, the number of defective light bulbs in a box of ten.

**Probability Mass Function:** The probability mass function of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function, i.e., p = P (X = x).

**Cumulative Distribution Function:** The cumulative distribution function of a random variable is a function giving the probability that the random variable X is less than or equal to x, for every value x, i.e. F = P(X £ x)

Enter the parameters (n) and (p), and (k), then click
the **Compute** buttons to get P = P(X = k) and F = P(X £ k).

n |
p |
k |
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P = | F = | |||||||||

For Technical Details, Back to:

Binomial Probability

Enter the parameters (r) and (p), and (k), then click
the **Compute** buttons to get P = P(X = k) and F = P(X £ k).

r |
p |
k |
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P = | F = | |||||||||

For Technical Details, Back to:

Negative-Binomial Probability