# 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.