Instructor: Anatolii Grinshpan

Office hours: Tu 11-1 & Fr 11-12, Korman 249, or by appointment, Korman 253.

Course information Academic
Calendar Grinstead & Snell History Tutoring center

Mar 31. Introduction to the
course. Discrete probability framework. Venn diagrams. Example.

April
2. Coin toss experiments. Simulations. Uniform
distribution. Bertrand’s paradox.

Reading:
Chapter 1. Problems: due April 9.

April
7. Monte Carlo. Buffon’s needle. Simulations. Continuous
density.

April
9. Continuous random variables. Cumulative
distribution function. Examples.

Reading:
Chapter 2. Problems: due April 16.

Apr 14.
Elementary combinatorics. Stirling’s
formula. Binomial coefficients. Inclusion-exclusion. Example.

Apr 16.
Simulations.
Poker hands. Bernoulli trials. Binomial distribution.

Reading:
Sections 3.1, 3.2. Problems: due April 23.

Apr 21.
Properties of binomial distribution. Conditional
probability (discrete case). Three-way
duel.

Apr 23.
Reverse tree. Monty Hall problem. Independence of events.

Reading:
Section 4.1. Problems.

Apr 28.
Exam 1
(Sections 1.1-3.2, 4.1).

Apr 30.
Joint distribution and independence of random variables. Independent trials
processes. Bayes’ formula. Likelihood ratio.
Conditional density.

Reading:
Sections 4.1, 4.2. Problems: due May 7.

May 5. Independence of continuous random
variables. Exponential distribution. Cauchy
density. Distribution of maximum.

May 7. Conditional and marginal
distributions. Poisson distribution. Gamma
function.

Reading:
Sections 4.2, 5.1, 5.2. Problems: due May
14.

May 12.
Marginal and conditional densities. Beta distribution. Random coin. Functions of a random variable. Example.

May 14.
Geometric distribution. Normal distribution.
Expected value.

Reading:
Sections 5.2, 6.1. Problems: due May 21.

May 19.
Expectation and variance. Examples. A
property of the mean.

May 21.
Convolution. Sums of random variables: binomial, geometric, uniform, normal.

Reading:
Sections 6.2, 6.3, 7.1, 7.2. Problems.

May 26.
Memorial Day.

May 28.
Exam 2
(Sections 4.2, 5.1-7.2).

June 2.
Law of Large Numbers. Chebyshev’s
inequality. Bernoulli’s theorem.

June 4.
de Moivre –
Laplace. Illustration. Example. Galton board. Central Limit Theorem.

Reading:
Sections 8.1, 8.2., 9.1-9.3. Problems.

June 9.
Moment generating functions. Proof
of the central limit theorem.

*June 12. Questions session
10-12, Lebow 134.*

June
13. Final exam: 10:30-12:30, GL 48 (all lectures).