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Chapter 18

# MATH 123 Chapter Notes - Chapter 18: Cumulative Distribution Function, Standard Deviation, Random Variable

by OC1682449

School

McGill UniversityDepartment

Mathematics and StatisticsCourse Code

MATH 123Professor

Sidney TrudeauChapter

18This

**preview**shows half of the first page. to view the full**2 pages of the document.**MATH 123 – Linear Algebra and Probability

Chapter 18: Probability and Calculus

Continuous Probability Models

Calculus is used in the study of probability. We focus on the idea of a random variable and its

connection to a probability density function and a cumulative distribution function.

There are four important concepts:

1. Expected value;

2. Variance;

3. Standard deviation;

4. Median.

𝐹(𝑥)= 𝑃(𝑋 ≤ 𝑥)= ∫ 𝑓(𝑡)𝑑𝑡

Expected Value and Variance of Continuous Random Variables

Expected value is the average value of a random variable that we would expect in the long run.

Variance is a measure of the spread of the values of a distribution.

Standard deviation is the square root of the variance.

Median is the value of a random variable for which there is a 50% probability of being larger

and a 50% probability of being smaller.

Special Probability Density Functions

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