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

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 123
• Professor: Sidney Trudeau

Document Summary

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: expected value, variance, standard deviation, median. (cid:4666)(cid:4667)=(cid:4666) (cid:4667)= (cid:1858)(cid:4666)(cid:4667)(cid:1856) 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. Integration techniques can be used to determine probabilities, expected value, and variance of continuous random variables. Three probability density functions have a wide range of applications: uniform, exponential, normal.