## MATH/STAT 3360 - Fall 2014

#### ## Probability This is the page where I post material related to the MATH/STAT 3360 course I am teaching in FALL 2014.

• Office hours: Monday 14:30-15:30, Wednesday 14:30-15:30, Thursday 14:30-15:30
• Office: 202 Chase 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/3360/2013/index.html. You may find some of the material there useful.
• Midterm Exam: Thursday 23rd October, in class. Here are last year's Practice midterm and model solutions and last year's midterm and model solutions.
• Here is the midterm. Here are the model solutions.
• Here is the formula sheet for the midterm. You will also be provided with a Normal distribution table. No notes are permitted in the examination. Scientific calculators are permitted, but not graphical calculators.
• Textbook: A First Course in Probability (Ninth Edition) by Sheldon Ross, published by Prentice Hall, 2013
• Final Exam: Monday 8th December, 8:30-11:30AM, Dalplex. Here are some Practice questions and model solutions.
• Here is the formula sheet for the final. You will also be provided with a Normal distribution table. No notes are permitted in the examination. Scientific calculators are permitted, but not graphical calculators.
• #### 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 previous years' homework sheets).

Week beginning Tuesday Thursday
1st September Introduction
8th 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
• 2.5 Sample Spaces of Equally Likely Events
• 15th September
• 2.5 Sample Spaces of Equally Likely Events (cont.)
• 2.6 Probability as a Continuous Set Function
• 2.7 Probability as a Measure of Belief
• 3.2 Conditional Probability
• 3.3 Bayes Formula
• 3.4 Independant Events
• 22nd September
• 3.5 P(.|F) is a probability
• 4.1 Random Variables
• 4.2 Discrete Random Variables
• 4.3 Expected Value
• 4.4 Expectation of a Function of a Random Variable
• 4.5 Variance
• 4.6 Bernoulli & Binomial Random Variables
• 4.7 Poisson Random Variables
• 29th September
• 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
• 6th October
• 5.4 Normal Random Variables
• 5.5 Exponential Random Variables
• 5.7 Distribution of a Function of a Random Variable
• 13th October Revision Chapters 1-5 Revision Chapters 1-5
20th October Revision Chapters 1-5

MIDTERM

EXAMINATION

27th 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
• 3rd 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
• 10th November REMEMBRANCE DAY
• 7.4 Covariance, Variance of Sums and Correlation
• 7.5 Conditional Expectation
• 7.6 Conditional Expectation and Prediction
• 17th 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
• 24th November
• 8.4 The Strong Law of Large Numbers
• 8.5 Other Inequalities (One-sided Chebyshev Inequality, Chernoff Bounds)
• Revision
1st December Revision END OF LECTURES

#### Homework

 Assignment 1 Due Thursday 18th September. Model Solutions Assignment 2 Due Thursday 25th September. Model Solutions Assignment 3 Due Thursday 2nd October. Model Solutions Assignment 4 Due Thursday 9th October. Model Solutions Assignment 5 Due Thursday 16th October. Model Solutions Assignment 6 Due Thursday 13th November. Model Solutions Assignment 7 Due Thursday 20th November. Model Solutions Assignment 8 Due Thursday 27th November. Model Solutions