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Chapter 18

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

Mathematics and Statistics
Course Code
MATH 123
Sidney Trudeau

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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(π‘₯)= 𝑃(𝑋 ≀ π‘₯)= ∫ 𝑓(𝑑)𝑑𝑑
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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