Instructor: Anatolii Grinshpan

Office hours: Tue 10-12 & Fri 10-11, Korman 249, or by appointment, Korman 253.

Course information Academic
Calendar Grinstead & Snell History Tutoring center

Sep 22. Introduction to the
course. Discrete probability framework. Venn diagrams. Monotonicity. Example.

Sep 24. De Méré’s bets.
Division
of stakes. Algebra with events. Tree
diagrams. Uniform distribution. Random
variables.

Reading:
Section
1.2. Problems: due October 1.

Sep 29.
Coin toss until first head. Continuous probability model. Probability as length, area, or mass.

Oct 1. Continuous uniform
distribution. Density.
Cumulative distribution.

Reading:
Section
2.2. Problems: due October 8.

Oct 6. The sum of two random numbers from [0, 1]. Permutations. Birthday problem. Binomial coefficients.

Oct 8. Poker hands. Bernoulli trials. Binomial distribution. Stirling’s formula.

Reading:
Sections
3.1, 3.2. Problems: due October 15.

Oct 13.
Columbus day.

Oct 15.
Binomial odds ratios. Fixed points of permutations. Inclusion-exclusion principle. Example.

Oct 20.
Discrete conditional probability. Reverse tree
diagrams. Monty Hall problem. Bayes’ formula.

Reading:
Section
4.1. Problems.

*Oct 21. Questions sessions: 10-12 (Korman 249), 4:40-6 (Curtis 456).*

Oct 22.
Midterm 1.

Oct 27.
Independence of events. Joint,
marginal, and conditional probability mass functions. Independence
of random variables.

Oct 29.
Continuous conditional probability. Joint, marginal
and conditional density functions. Example. Mass vs density.

Reading:
Sections
4.1, 4.2. Problems: due November 3.

Nov 3. Multinomial, geometric, and negative binomial
distributions. Poisson distribution. Example.

Nov 5. Poisson counts and exponential waiting
times. Cauchy density. Normal density. Functions of random variables.

Reading:
Chapter
5. Problems: due November 10.

Nov 10.
Expected value and variance (discrete case).

Nov 12.
Expected value and variance (continuous case).

Reading:
Chapter
6. Problems: due November 17.

Nov 17.
Sums of discrete independent variables. Convolution.
Binomial as a
convolution.

Reading:
Section
7.1. Problems.

*Nov 18. Questions sessions: 10-12 (Korman 249), 5-6:20 (Curtis 250A).*

Nov 19.
Midterm 2.

Nov 24.
Sum of binomials. Sum of continuous variables: uniform, normal.

Reading:
Section
7.2.. Problems: due December 3.

Nov 26.
Thanksgiving break.

Dec 1. Chebyshev
inequality. Law of
Large Numbers.

Reading:
Chapter
8.

Dec 3. De Moivre
– Laplace. Galton board,
spike plots. Central
Limit Theorem. Local Limit Theorem.

*Dec 8. Questions session: 6-7:30
(Randell 114)*

*Dec 9. Office hours Noon-2 (Korman 249)*

Dec 10.
Final exam (all lectures): 1-3PM, Lebow 135.