Statistics and Probability Dictionary

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Continuous Probability Distribution

If a random variable is a continuous variable , its probability distribution is called a continuous probability distribution .

A continuous probability distribution differs from a discrete probability distribution in several ways.

  • The probability that a continuous random variable will assume a particular value is zero.
  • As a result, a continuous probability distribution cannot be expressed in tabular form.
  • Instead, an equation or formula is used to describe a continuous probability distribution.

The equation used to describe a continuous probability distribution is called a probability density function (pdf). All probability density functions satisfy the following conditions:

  • The random variable Y is a function of X; that is, y = f(x).
  • The value of y is greater than or equal to zero for all values of x.
  • The total area under the curve of the function is equal to one.

The charts below show two continuous probability distributions. The chart on the left shows a probability density function described by the equation y = 1 over the range of 0 to 1 and y = 0 elsewhere. The chart on the right shows a probability density function described by the equation y = 1 - 0.5x over the range of 0 to 2 and y = 0 elsewhere. The area under the curve is equal to 1 for both charts.

y = 1 y = 1 - 0.5x

The probability that a continuous random variable falls in the interval between a and b is equal to the area under the pdf curve between a and b. For example, in the first chart above, the shaded area shows the probability that the random variable X will fall between 0.6 and 1.0. That probability is 0.40. And in the second chart, the shaded area shows the probability of falling between 1.0 and 2.0. That probability is 0.25.

See also:   Probability Distributions | Tutorial: Discrete and Continuous Random Variables