## MATH/STAT 3360 - Fall 2013

#### ## Probability This is the page where I post material related to the MATH/STAT 3360 course I am teaching in FALL 2013.

• 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/3360/2012/index.html. You may find some of the material there useful.
• Midterm Exam: Thursday 24th October, in class.Here are some practice questions for the midterm. Here are the model solutions. Here is the formula sheet for the midterm.
• Textbook: A First Course in Probability (Ninth Edition) by Sheldon Ross, published by Prentice Hall, 2013
• Final Exam: Saturday 14th December, 08:30 am, Dalplex.Here are some practice questions for the final. Here are the model solutions. Here is the formula sheet for the final.
• #### 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
2nd September Introduction
9th 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
• 16th 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
• 23rd 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
• 30th September
• 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
• 7th 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
• 14th October
• 5.5 Exponential Random Variables
• 5.7 Distribution of a Function of a Random Variable
• Revision Chapters 1-5
21st October Revision Chapters 1-5

MIDTERM

EXAMINATION

28th 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
• 4th 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
• 11th November STUDY DAY
• 7.4 Covariance, Variance of Sums and Correlation
• 7.5 Conditional Expectation
• 7.6 Conditional Expectation and Prediction
• 18th 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
• 25th November
• 8.4 The Strong Law of Large Numbers
• 8.5 Other Inequalities (One-sided Chebyshev Inequality, Chernoff Bounds)
• Revision
2nd December Revision END OF LECTURES

#### Homework

 Assignment 1 Due Thursday 19th September. Model Solutions Assignment 2 Due Thursday 26th September. Model Solutions Assignment 3 Due Thursday 3rd October. Model Solutions Assignment 4 Due Thursday 10th October. Model Solutions Assignment 5 Due Thursday 17th October. Model --> Assignment 6 Due Thursday 14th November. Model Solutions Assignment 7 Due Thursday 21st November. Model Solutions Assignment 8 Due Thursday 28th November. Model Solutions