# Math 311 – Probability and Statistics, Spring 2014

Instructor: Anatolii Grinshpan

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

Course information  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).