Trent University

Mathematics 1550H

*Probability I: Introduction to Probability*

MATH 1550H is an introductory course in probability theory, covering the basics of both discrete and continuous probability distributions. Please note that it does **not** count as the Introductory Statistics course required by some professional schools.

**Prerequisite:** MATH 1005H - Applied Calculus, or MATH 1110H - Calculus I: Limits, Derivatives, and Integrals, or permission of the instructor.

As a minimum, the part of the course dealing with continuous probability distributions requires knowledge of limits, derivatives, and integrals (through the basic substitution rule and integration by parts), as applied to functions constructed from polynomials and exponential functions.

- Summer 2023 MATH 1550H Course Outline
- Some general advice for first-year mathematics students: Enjoying Math!
- Textbook: Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. [Electronic edition prepared by Peter G. Doyle.]

Suggested homework exercises from the textbook.

Answers to odd-numbered exercises from the textbook. - Some Common Distributions
- Cumulative Standard Normal Table
- Assignment # 1,
2,
3,
4,
5,
6,

and Solutions to Assignment # 1, 2, 3, 4, 5, 6. - Quiz # 0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,

and Solutions to Quiz # 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

(Note that the quizzes were one-day mini-assignments.) - Test and Solutions to the Test
- Final Examination and Solutions to the Final Examination
- Lecture videos (webm format).
- 2023-06-19 - Not recorded. The lecture covered basic discrete probability and related counting techniques.
- 2023-06-21 - Managed to record the intermissions instead of the middle part of the lecture.

Part a -*Recap of 2023-06-19 and the hat check problem.*

Parts b and c -*The intermissions, so you can see what was on the board.*The missing middle introduced tree diagrams and random variables.

Part d -*An example of a random variable problem which it was convenient to use a tree-diagram to analyze.* - 2023-06-26

Part a -*The basics of events and conditional probability.*

Part b -*The Rule of Total Probability and Bayes' Theorem.*

Part c -*The basics of continuous probability.* - 2023-06-28 - Only two parts to this lecture.

Part a -*A recap of continuous probability, plus some examples.*

Part b -*More examples involving continuous probability, in part to practice the integration techniques required.* - 2023-07-05

Part a -*A recap of the basics of random variables, plus a nasty example.*

Part b -*A very brief look at cumulative probability functions, followed by expected values of discrete random variables.*

Part c -*The basics of expected value for continuous random variables.* - 2023-07-10

Part a -*A quick recap of expected values, and then on to variance.*

Part b -*Some general properties of expected value and variance.* - 2023-07-12

Part a -*Some standard discrete distributions I.*

Part b -*Some standard discrete distributions II.* - 2023-07-17

Part a -*Continuous uniform and exponential distributions.*

Part b -*The standard normal distribution.*

Part c -*Normal distributions.* - 2023-07-19

Part a -*Markov's and Chebushev's Inequalities.*

Part b -*Independently and identically distributed random variables, the Laws of Large Numbers, and the Central Limit Theorem.*

Part c -*Using the Central Limit Theorem.* - 2023-07-24

Part a -*Bivariate discrete distributions and covariance.*

Part b -*Basic properties of covariance.*

- Winter 2023 MATH 1550H Course Outline
- No official textbook, but use was made of the following, especially the first:
- MATH-1550H: Introduction to Probability Notes, developed over several years of teaching the course by John Talboom and Aras Erzurumluoglu.
- Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. [Electronic edition prepared by Peter G. Doyle.]

- Weekly Exercise Sets (for practice), by John Talboom

Exercise Set # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,

and Solutions to Exercise Set # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 - Weekly Seminar Sets (for practice), by John Talboom

Seminar Set # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,

and Solutions to Seminar Set # 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 - Solutions to the weekly Mini-Assignments

# 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 - Test # 1,
2,

and Solutions to Test # 1, 2 - Lecture videos, in a variety of formats. (I had both hardware and sodtware problems, plus lost a week to illness.)
- 2023-01-09 - Some organizational bits and counting.

Part a, b, c - 2023-01-11 - Mainly binomial coefficients and identities.

Recording failed. - 2023-01-16 - A bit more on binomial coefficients and then on to the basics od probability.

Video artifacts in both parts and loss of audio in part b. Part a, b - 2023-01-18 - Mostly about events.

Part a - 2023-01-23 - The hat-check problem, followed by conditional probability, independence, and Bayes' Theorem.

Part a, b - 2023-01-25 - An application of Bayes' Theorem.

Part a - 2023-01-30 - Discrete random variables and probability distribution functions.

Recording failed for part b. Part a - 2023-02-01 - Cumulative distribution functions for discrete random variables.

Part a - 2023-02-06 - The basics of continuous probablity. Originally posted on 2020-07-03; reposted due to the instructor's illness.

Video and notes. - 2023-02-13 - Cumulative probability functions for continuous random variables in part a, and discrete joint probability functions in part b.

Part a, b - 2023-02-15 - Mostly about continuous joint probability density functions.

Part a - 2023-03-06 - Expected value for discrete (part a) and continuous (part b) random variables. Recorded at home due to instructor's illness.

Part a video and notes, and Part b video and notes - 2023-03-08 - More on expected value. Recorded at home due to instructor's illness.

video and notes - 2023-03-13 - A quick review of expected values, followed by variance and Markov's and Chebyshev's Inequalities.

Part a, b - 2023-03-20 - Covariance of two jointly distributed random variables, discrete in part a and continuous in partb.

Part a, b - 2023-03-22 - A quick look at expected values for conditional probabilities, follows by a look at Bernoulli trials and the binomial distribution.

Part a - 2023-03-27 - Several common discrete distributions and their expected values and variances.

Part a, b

Handout: Some Common Probability Distributions - The Short Form - 2023-03-29 - Mainly on exponential distributions.

Part a - 2023-04-03 - The standard normal distribution and why it rules, and the Laws of Large Numbers.

Part a, b

Handouts: A standard normal table and another standard normal table - 2023-04-05 - The Central Limit Theorem.

Part a

- 2023-01-09 - Some organizational bits and counting.

- Summer 2020 MATH 1550H Course Outline
- Enjoying Math!
- The textbook: Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. [Electronic edition prepared by Peter G. Doyle.]
- Answers to Odd-Numbered Exercises
- Suggested Homework Problems
- Lectures and Notes:
- The Basics of Discrete Probability: Video, Notes
- Discrete Probability: Tree Diagrams and Some Common Distributions: Video, Notes
- Permutations and Combinations: Video, Notes
- VideoSome Uses of Permutations and Combinations: , Notes
- Continuous Probability: The Basics: Video, Notes
- Conditional Probability: Video, Notes
- A Few Common Distributions: Video, Notes
- Expected Value: Video, Notes
- Variance and Standard Deviation: Video, Notes
- Example: A pretty easy continuous density function or two: Video, Notes
- Example: A pretty hard continuous density function: Video, Notes
- Sums of Independent Random Variables: Video, Notes
- Two Inequalities: Video, Notes
- Averages of Random Variables: Video, Notes
- Covariance: Video, Notes
- Just for fun! Why the standard normal density is a valid density: Video, Notes

- Additional Notes:
- Some Common Probability Distributions – The Short Form [Just the most vital facts about each distribution.]
- Cumulative Standard Normal Table - an alternative to the table in the textbook.

- Assignment # 1,
2,
*e*, 3, 4, 5

and Solutions to Assignment # 1, 2,*e*, 3, 4, 5. - Quiz # 1,
2,
3,
4,
5,
6

and Solutions to Quiz # 1, 2, 3, 4, 5, 6 - Final Examination and Solutions to the Final Examination

- Winter 2016 MATH 1550H Course Outline
- Enjoying Math!
- The textbook: Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. [Electronic edition prepared by Peter G. Doyle.]
- Some Common Distributions
- Cumulative Standard Normal Table
- Assignment # 1,
2,
3,
4,
5,
6,
2π,
7,
8,
9,
10,
11

and Solutions to Assignment # 1, 2, 3, 4, 5, 6, 7, 8, 9 - Test # 1, 2 and Solutions to Test # 1, 2
- Exam Review handout by Samantha Leigh.
- Final Examination and Solutions to the Final Examination

- Summer 2017 MATH 1550H Course Outline
- Enjoying Math!
- The textbook: Introduction to Probability by Charles M. Grinstead and J. Laurie Snell. [Electronic edition prepared by Peter G. Doyle.]
- Some Common Distributions
- Cumulative Standard Normal Table
- Assignment # 1, 2, 3, 4, 5, 6 and Solutions to Assignment 1, 2, 3
- Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination and Solutions to the Final Examination

- Winter 2016 MATH 1550H Course Outline
- Enjoying Math!
- Some common distributions
- Cumulative Standard Normal Table
- Assignment # 1,
2,
*e*, 3, 4 and Solutions to Assignment # 1, 2, 3 - Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination and Solutions to the Final Examination

- Summer 2016 MATH 1550H Course Outline
- Enjoying Math!
- Some Common Distributions
- Cumulative Standard Normal Table
- Assignment # 1, 2, 3, 4, 5, ε and Solutions to Assignment # 1
- Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination

- Winter 2016 MATH 1550H Course Outline
- Enjoying Math!
- Assignment # 1,
2,
3,
4

Solutions to Assignment # 1, 2, 3, 4 - Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination
- Some common distributions
- Cumulative Standard Normal Table

- Summer 2015 MATH 1550H Course Outline
- Enjoying Math!
- Cumulative Standard Normal Table
- Some common distributions
- Assignment # 1, 2, 3, 4, 5, 6
- Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination and Solutions to the Final Examination

- Winter 2015 MATH 1550H Course Outline
- Winter 2015 MATH 1550H Readings and Schedule
- Assignment # 1, 2, 3, 4
- Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination
- Cumulative Standard Normal Table

Please note that iterations of MATH 1550H below used different texbooks from the one used above (and from each other, too), and did some of the material in a substantially different order.

- Summer 2014 MATH 1550H Course Outline
- Homework Problems
- Assignment # 1,
2,
3,
4,
5,
6

Solutions to Assignment # 1, 2, 3, 4, 5 - Quizzes and Solutions to the Quizzes
- Test and Test Solutions
- Final Examination and Solutions to the Final Examination

- Summer 2013 MATH 1550H Course Outline
- Homework Problems
- Assignment # 1,
2,
3,
4,
5,
6

Solutions to Assignment # 1, 2, 3 - Quizzes and Solutions to the Quizzes
- Practice Test, Test, and Test Solutions
- Practice Exam, Final Examination, and Solutions to the Final Examination

Maintained by Stefan Bilaniuk. Last updated 2023-08-01.