## Mathematics 206

### Mathematical Statistics

Length of Course: 14 weeks

Classroom Hours per Week: 4

Number of Credits: 3

Prerequisite: 12 credits

Corequisite:  Mathematics 114

Text: Mathematical Statistics with Applications,Wackerly et al. Latest Edition

### Course Description

A calculus-based introduction to probability and mathematical statistics.

### Course Outline:

Length Description

Week 1

Probability: Introduction, Probability and inference, Review of set notation, A probabilistic model for an experiment: the discrete case

Week 2

Probability: Calculating the probability of an event: the sample-point method, Tools for counting sample points, Conditional probability and the independence of events, Two laws of probability

Week 3

Probability: Calculating the probability of an event: the event-decomposition method, The Law of total probability, Bayes’ rule, Numerical events and random variables, Random sampling

Week 4

Discrete Random Variables: Basic definition, The probability distribution for a discrete random variable, The expected value of a random variable, The Binomial probability distribution

Week 5

Discrete Random Variables: The Geometric probability distribution, The Negative Binomial probability distribution, The Hypergeometric probability distribution, The Poisson probability distribution

Week 6

Discrete Random Variables: Moments and moment-generating functions, Probability-generating functions, Tchebysheff’s theorem

Week 7

Continuous Random Variables: The probability distribution for a continuous random variable, Expected values, The Uniform probability distribution

Week 8

Continuous Random Variables: The Normal probability distribution, The Gamma probability distribution

Week 9

Continuous Random Variables: The Beta probability distribution, Tchebysheff’s theorem

Week 10

Multivariable Probability Distribution: Bivariate and multivariate probability distribution, Marginal and conditional probability distribution, Independent random variables

Week 11

Multivariable Probability Distribution: The expected value, Special theorems, The covariance of two random variables

Week 12

Multivariable Probability Distribution: The expected value and variance of linear functions of random variables, The Multinomial probability distribution, The Bivariate Normal distribution (optional)

Week 13

Review

Week 14

Final Exam

### Evaluation:

10-20% Quizzes and Homework Midterm Exam(s) Final Exam

### Instructors

Arman Ahmadieh B.Sc., M.Sc. (Sharif University of Technology)
Hayri Ardal, B.Sc.(Bogazici), Ph.D.(Simon Fraser)
Kim Peu Chew, B.Sc. (Nanjing), M.A., Ph.D. (British Columbia)
Rika Dong, B.Sc. (Simon Fraser), M.Sc. (Regina)
Sam Ekambaram, B.Sc., M.Sc. (Madras), M.Sc., Ph.D. (Simon Fraser)
Himadri Ganguli, B.Sc., M.Sc. (Chennai), Ph.D. (Simon Fraser)
Peter Hurthig, B.Sc., M.Sc. (British Columbia)