Probability Density Functions of Continuous Random Variables

Study Notes

Probability Density Function vs. Probability Mass Function

A probability density function (PDF) is used for continuous random variables, whereas a probability mass function (PMF) is used for discrete random variables.

Characteristics of a Probability Density Function

A probability density function (PDF) is a non-negative function that satisfies the property that the integral over the entire range of the variable is equal to 1.
The area under the curve of a PDF represents the probability of the event.

Normalizing a Probability Density Function

The purpose of normalizing a probability density function is to ensure that the total probability over all possible values of the random variable is equal to 1.

Examples of Continuous Random Variables

The time until a component fails is an example of a continuous random variable.
The height of a person in a population is another example of a continuous random variable.

Probability Density Function and Cumulative Distribution Function

The cumulative distribution function (CDF) is the integral of the probability density function (PDF) from negative infinity to a specific point.
The PDF can be obtained by differentiating the CDF with respect to the variable.

Description

This quiz covers the basics of probability density functions of continuous random variables, including their differences from probability mass functions, characteristics, and relationships with cumulative distribution functions.