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Chapter 18

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

Department
Mathematics and Statistics
Course Code
MATH 123
Professor
Sidney Trudeau
Chapter
18

This 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