## Tentative Syllabus  Math 477:01 -- Fall 2007

### Section numbers refer to A First Course in Probability, Seventh Edition, by Sheldon Ross.

Date Sections Topics
9/4 1.1--1.5 Combinatorics
9/7 1.6--2.3 Indistinguishable objects; axioms of probability
9/11 2.4, 2.5 Inclusion/exclusion formula; equally likely outcomes
9/14 2.5 More examples; Stirling's approximation
9/18 3.1--3.3 Conditional probability and Bayes' formula
9/21 3.4 Independent events
9/25 3.4, 3.5 Repeated independent trials
9/28 4.1--4.2 Random variables and distribution functions
10/2 4.3--4.5 Expectation and variance of discrete random variables
10/5 4.6, 4.8.1 Bernoulli, binomial, and geometric random variables
10/9 EXAM 1 All material covered through lecture of 10/2
10/12 4.7, 4.9.2, 4.9.3 Poisson, negative binomial, and hypergeometric random variables
10/16 5.1, 5.2 Continuous random variables; expectation, variance
10/19 5.3--5.5 Uniform, exponential, and normal random variables
10/23 5.4.1 Normal approximation to binomial random variables
10/26 5.6.1, 5.7 Gamma random variable; functions of a random variable
10/30 6.1 Joint distributions of several random variables
11/2 6.2 Independent random variables
11/6 6.3 Sums of independent random variables
11/9 7.1--7.3 Linearity of expectation
11/13 EXAM 2 All material covered through lecture of 11/6
11/16 7.4 Covariance and correlation
11/21 6.4, 6.5 Conditional distributions
11/27 7.5 Conditional expectation
11/30 7.7 Moment generating functions
12/4 8.1--8.2 Markov and Chebyshev inequalities; weak law of large numbers
12/7 8.3 The central limit theorem
12/11 8.3 Proof of the central limit theorem; examples.
12/18 FINAL EXAM 8:00 A.M.--11:00 A.M.