Dr. Z's Introduction to Probability Handouts

By DORON ZEILBERGER

These are the handouts I gave out when I taught "Introduction to Probability", during the Fall 2017 semester.

Lecture 1: Counting

Lecture 2: What is Probability? Counting vs. Probability

Lecture 3: Sample spaces having equally likely outcomes.

Lecture 4: Conditional Probability and Independence; Bayes's Formula

Lecture 5: Independent events.

Lecture 6:Random Variables

Lecture 7: Expectation and Variance

Lecture 8: The Bernoulli and Binomial Random Variables

Lecture 9: The Poisson Random Variable

Lecture 10:Other Discrete Probability Distributions; Linearity of Expectation

Lecture 11: Continuous Random Variables; Their Expectation and Variance

Lecture 12:The Uniform Distribution and the Normal Distribution.

Lecture 13: The Exponential Distribution

Lecture 14: Joint Distribution Functions

Lecture 15:Independent Random Variables and their Sums

Lecture 16: Conditional Distributions

Lecture 17: Expectation of Sums of Random Variables

Lecture 18: Probability Generating Functions; The Gambler's Ruin Problem.

Lecture 19: Covariance, Variance of Sums, and Correlations

Lecture 20: Conditional Expectation

Lecture 21:Moment Generating Functions

Lecture 22:Chebyshev's Inequality and the Weak Law of Large Numbers

Lecture 23: The Central Limit Theorem and The Strong Law of Large Numbers.

Exams

Here are the answers.