## MATH/STAT 3360 - Fall 2012

#### ## Probability This is the page where I post material related to the MATH/STAT 3360 course I am teaching in FALL 2012.

• Office hours: Monday 13:30-14:30, Wednesday 13:30-14:30, Thursday 14:30-15:30
• Office: 251 Chase building (on the 2.5th floor - you need to take the stairs at the South end of the building.)
• If you want to come to my office at a different time please email me:tkenney@mathstat.dal.ca
• The website for last year's course is www.mathstat.dal.ca/~tkenney/3360/2011/index.html. You may find some of the material there useful.
• Midterm Exam: Thursday 25th October, in class.
• here is the formula sheet for the midterm
• here are the model solutions for the midterm
• Textbook: A First Course in Probability (Eighth Edition) by Sheldon Ross, published by Prentice Hall, 2010
• Final Exam: TBA.
• #### Handouts

Course Handout

#### Planned material

Lecture time is limited, so I plan to use it explaining concepts and giving examples, rather than reading the textbook. Therefore, to get the most out of each lecture, you should read the relevant material before the lecture. Here is the list of what I expect to cover in each lecture. This is subject to change - make sure to check regularly for changes.

Here are some questions on these topics that we may go over in class (taken mostly from last year's homework sheets).

Week beginning Tuesday Thursday
3rd September Introduction
10th September
• 1.2 Basic Principle of Counting (Multiplication Principle, Rule of product)
• 1.3 Permutations
• 1.4 Combinations
• 1.5 Multinomial Coefficients
• 2.2 Sample Spaces & events
• 2.3 Axioms of Probability
• 2.4 Simple Propositions
• 17th September
• 2.5 Sample Spaces of Equally Likely Events
• 2.6 Probability as a Continuous Set Function
• 2.7 Probability as a Measure of Belief
• 3.2 Conditional Probability
• 3.3 Bayes Formula
• 24th September
• 3.4 Independant Events
• 3.5 P(.|F) is a probability
• 4.1 Random Variables
• 4.2 Discrete Random Variables
• 4.3 Expected Value
• 1st October
• 4.4 Expectation of a Function of a Random Variable
• 4.5 Variance
• 4.6 Bernoulli & Binomial Random Variables
• 4.7 Poisson Random Variables
• 4.9 Expectation of Sums of Random Variables
• 4.10 Cumulative Distribution Functions
• 8th October
• 5.1 Continuous Random Variables
• 5.2 Expectation and Variance of Continuous Random Variables
• 5.3 Uniform Random Variables
• 5.4 Normal Random Variables
• 15th October
• 5.5 Exponential Random Variables
• 5.7 Distribution of a Function of a Random Variable
• Revision Chapters 1-5
22nd October Revision Chapters 1-5

MIDTERM

EXAMINATION

29th October
• 6.1 Joint Distribution Functions
• 6.2 Independent Random Variables
• 6.3 Sums of Independent Random Variables
• 6.7 Joint Probability Distribution of Functions of Random Variables
• 5th November
• 6.4 Conditional Distributions (Discrete)
• 6.5 Conditional Distributions (Continuous)
• 7.2 Expectation of Sums of Random Variables
• 7.3 Moments of the Number of Events that Occur
• 12th November STUDY DAY
• 7.4 Covariance, Variance of Sums and Correlation
• 7.5 Conditional Expectation
• 7.6 Conditional Expectation and Prediction
• 19th November
• 7.7 Moment Generating Functions
• 7.8 Additional Properties of Normal Random Variables
• 8.2 Markov's Inequality, Chebyshev's Inequality and the Weak Law of Large Numbers
• 8.3 The Central Limit Theorem
• 26th November
• 8.4 The Strong Law of Large Numbers
• 8.5 Other Inequalities (One-sided Chebyshev Inequality, Chernoff Bounds)
• Revision
3rd December Revision END OF LECTURES

#### Homework

 Assignment 1 Due Thursday 20th September. Model Solutions Assignment 2 Due Thursday 27th September. Model Solutions Assignment 3 Due Thursday 4th October. Model Solutions Assignment 4 Due Thursday 11th October. Model Solutions Assignment 5 Due Thursday 18th October. Model Solutions Assignment 6 Due Thursday 15th November. Model Solutions Assignment 7 Due Thursday 22nd November. Model Solutions Assignment 8 Due Thursday 29th November. Model Solutions