Probability

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

1. Probability can be calculated using improper integrals when dealing with continuous random variables.
2. The probability density function (PDF) must integrate to 1 over its entire range.
3. The cumulative distribution function (CDF) gives the probability that a random variable is less than or equal to a certain value.
4. In some cases, improper integrals are used to find the expected value (mean) or variance of a probability distribution.
5. Understanding convergence of improper integrals is crucial for evaluating probabilities in unbounded intervals.

Review Questions

• What role do improper integrals play in calculating probabilities for continuous random variables?
• How do you use the PDF and CDF in evaluating probabilities?
• Why is it important for the PDF to integrate to 1 over its entire range?

Related terms

Improper Integral:

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.