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A mathematical function can be used to model the frequencies and probabilities of occurrences over time. A discrete probability distribution function associates a list of probabilities with each possible value of a discrete random variable. The probability distribution function is thus used to model the probabilities of a discrete random variable and is also known as a probability mass function . The probabilities of a continuous random variable are modelled using continuous distribution functions, also known as probability density functions (pdf's).

The following are particularly important forms of the probability distribution function.

This discrete probability density function models experiments that have only two possible outcomes. The probability of success is p and the probability of failure is q =1- p . The pdf models the probability that we will observe r sucesses and n - r failures in a total of n -trials.

Graph of the probability distribution function and the cumulative probability distribution function (redrawn from (External Link) using matlab)

From the example above, what is the probability that in 20-trials there are exactly six successes?

The probability that there are exactly six successes is 0.04

References:

  • Random Variables and their Probability Density and Distribution Functions, (External Link) (last accessed February 2006)
  • NCAR Advanced Study Program (External Link) (last accessed February 2006)

Co-Author: Mookho Tsilo

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Source:  OpenStax, Estimation theory. OpenStax CNX. May 14, 2006 Download for free at http://cnx.org/content/col10352/1.2
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