Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Probability measures the likelihood of an event occurring, expressed as a number between 0 and 1. It is a fundamental concept in both pure and applied mathematics, often used to model uncertainty.
5 Must Know Facts For Your Next Test
Probability can be calculated using improper integrals when dealing with continuous random variables.
The probability density function (PDF) must integrate to 1 over its entire range.
The cumulative distribution function (CDF) gives the probability that a random variable is less than or equal to a certain value.
In some cases, improper integrals are used to find the expected value (mean) or variance of a probability distribution.
Understanding convergence of improper integrals is crucial for evaluating probabilities in unbounded intervals.
An integral where either the interval of integration is infinite or the integrand has an infinite discontinuity.
Probability Density Function (PDF): A function that describes the likelihood of a random variable taking on a particular value, with its integral over all possible values equal to 1.
Cumulative Distribution Function (CDF): A function that represents the probability that a random variable will take on a value less than or equal to a given point.