## MATH/STAT 3360 - Fall 2011

#### ## Probability This is the page where I post material related to the MATH/STAT 3360 course I am teaching in FALL 2011.

• Office hours: (subject to change) Monday 11:00-12:00, Tuesday 11:00-12:00, 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 course was lectured last year by Prof. A. Sarhan. His website www.mathstat.dal.ca/~asarhan/stat 3360/stat3360.html contains some material from last year, which you may find a useful reference.
• Midterm Exam: Thursday 27th October, in class. Here is a sample midterm, and Here are model solutions. Here is the formula sheet for the midterm exam. Here are the model solutions for the midterm examination.
• Textbook: A First Course in Probability (Eighth Edition) by Sheldon Ross, published by Prentice Hall, 2010
• Final Exam: Friday 9th December 15:30-18:30, Dalplex.
• Here is a sample final exam. Here are the model solutions. Here is the formula sheet for the final exam.

#### 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.

Week beginning Tuesday Thursday
5th September Introduction
12th September
• 1.2 Basic Principle of Counting (Multiplication Principle, Rule of product)
• 1.3 Permutations
• 1.4 Combinations
• 1.5 Multinomial Coefficients
• 19th September
• 2.2 Sample Spaces & events
• 2.3 Axioms of Probability
• 2.4 Simple Propositions
• 2.5 Sample Spaces of Equally Likely Events
• 2.6 Probability as a Continuous Set Function
• 2.7 Probability as a Measure of Belief
• 26th September
• 3.2 Conditional Probability
• 3.3 Bayes Formula
• 3.4 Independant Events
• 3.5 P(.|F) is a probability
• 3rd October
• 4.1 Random Variables
• 4.2 Discrete Random Variables
• 4.3 Expected Value
• 4.6 Bernoulli & Binomial Random Variables
• 4.7 Poisson Random Variables
• 10th October
• 4.4 Expectation of a Function of a Random Variable
• 4.5 Variance
• 4.9 Expectation of Sums of Random Variables
• 4.10 Cumulative Distribution Functions
• 5.1 Continuous Random Variables
• 5.2 Expectation and Variance of Continuous Random Variables
• 5.3 Uniform Random Variables
• 17th October
• 5.4 Normal Random Variables
• 5.5 Exponential Random Variables
• 5.7 Distribution of a Function of a Random Variable
• Revision Chapters 1-5
24th October Revision Chapters 1-5

MIDTERM

EXAMINATION

31st 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
• 7th November
• 6.4 Conditional Distributions (Discrete)
• 6.5 Conditional Distributions (Continuous)
• STUDY DAY
14th November
• 7.2 Expectation of Sums of Random Variables
• 7.3 Moments of the Number of Events that Occur
• 7.4 Covariance, Variance of Sums and Correlation
• 7.5 Conditional Expectation
• 7.6 Conditional Expectation and Prediction
• 21st 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
• 28th November
• 8.4 The Strong Law of Large Numbers
• 8.5 Other Inequalities (One-sided Chebyshev Inequality, Chernoff Bounds)
• Revision
5th December Revision END OF LECTURES

#### Homework

 Assignment 1 Due Thursday 22nd September. Model Solutions Assignment 2 Due Thursday 29th September. Model Solutions Assignment 3 Due Thursday 6th October. Model Solutions Assignment 4 Due Thursday 13th October. Model Solutions Assignment 5 Due Thursday 20th October. Model Solutions Assignment 6 Due Thursday 17th November. Model Solutions Assignment 7 Due Thursday 24th November. Model Solutions Assignment 8 Due Thursday 1st December. Model Solutions