### The Common Discrete Probability Functions

This is a companion Web site to
P-values for the Popular Distributions

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham

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)

### Binomial Probability

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 P = F =

For Technical Details, Back to:
Binomial Probability ### Negative-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 P = F =

For Technical Details, Back to:
Negative-Binomial Probability ### Geometric Probability

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

 p k P = F =

For Technical Details, Back to:
Geometric Probability ### Poisson Probability

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

 l k P = F =

For Technical Details, Back to:
Poisson Probability ### Hypergeometric Probability

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

 M N n k P = F =

For Technical Details, Back to:
Hypergeometric Probability

Back to:
Statistical Thinking for Decision Making

Professor Hossein Arsham