Mathematical Theory of Probability

Rutgers MATH 477, Spring 2019.

daniel.krashen+prob@gmail.com

Lecture 1: Combinatorial analysis, part 1.
Lecture 2: Combinatorial analysis, part 2. Introduction to probability.
Lecture 3: Inclusion-exclusion, equally likely outcomes.
Lecture 4: Conditional probability, part 1.
Lecture 5: Conditional probability, part 2.
Lecture 6 (substitute, no notes): Independence.
Lecture 7 (substitute, no notes): Conditional probability as probability.
Lecture 8: Conditional probability wrap up, introduction to random variables.
Lecture 9 (no in-class worksheet): Expected values, variance, Bernoulli and Poisson variables.
Lecture 10: A bestiary of random variables.
Lecture 11: Binomial expectation and variance.
Lecture 12: Introduction to continuous random variables.
Lecture 13: Introduction to continuous random variables, part 2.
Lecture 14: Joint probability distributions.
Lecture 15: Dropping the ball: the normal distribution.
Lecture 16: Mostly sums of random variables.
Lecture 17: More sums of random variables and the gamma distribution.
Lecture 18: Expected value of functions of random variables, linearity of expectation.
Lecture 19: More linearity of expectation.
Lecture 20: Conditional expectation.
Lecture 21: Probability generating functions.
Lecture 22: Review.
Lecture 23: Variance, covariance and moments.
Lecture 24: Moment generating functions and the central limit theorem.