Random Variables, Means, Variance, and Standard Deviations in Probability and Statistics

Learn about random variables, probability distributions, and key statistical concepts in this 53-minute video lecture. Explore the fundamentals of random variables as functions on probability spaces and their associated probability distributions. Discover how to calculate and interpret three crucial statistical measures: mean (expected value), variance, and standard deviation. Examine practical examples, including a lottery scenario, to reinforce your understanding of these essential probability and statistics concepts.

Random variables
Three numbers associated to a random variable X
Probability distribution of a random variable
Example; lottery example
Expected value / mean
Variance
Formula for variance
Standard deviation