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key term - Probability density function

Definition

A probability density function (PDF) describes the likelihood of a continuous random variable taking on a particular value. The area under the PDF curve over an interval represents the probability of the variable falling within that interval.

5 Must Know Facts For Your Next Test

  1. The integral of a PDF over its entire range is equal to 1.
  2. A PDF must be non-negative for all possible values of the random variable.
  3. Improper integrals are often used when calculating probabilities involving PDFs with infinite bounds.
  4. The mean (expected value) of a continuous random variable can be found by integrating the product of the variable and its PDF over all possible values.
  5. A cumulative distribution function (CDF) is obtained by integrating the PDF from negative infinity to a specific value.

Review Questions

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