This course is designed to provide students with a comprehensive introduction to probability models. Topics covered include:
- The basics of probability theory
- Discrete and continuous random variables
- Joint distributions and conditional probability
- Bayesian inference
- Applications of probability models
Prerequisites:
- STAT 20 or STAT 21 or STAT 24 or STAT 25A or equivalent
- Math 1A, Math 1B, and Math 54 or equivalent
Grading:
- Homework assignments (20%)
- Midterm exam (30%)
- Final exam (50%)
Textbook:
- Probability Models by Sheldon Ross, 10th Edition
Course Outline:
Week 1: Introduction to Probability
- What is probability?
- The axioms of probability
- Conditional probability and independence
Week 2: Discrete Random Variables
- Bernoulli and binomial distributions
- Poisson distribution
- Hypergeometric distribution
Week 3: Continuous Random Variables
- Uniform distribution
- Exponential distribution
- Normal distribution
Week 4: Joint Distributions
- Joint distributions of discrete random variables
- Joint distributions of continuous random variables
- Marginal and conditional distributions
Week 5: Bayesian Inference
- Bayes’ theorem
- Applications of Bayesian inference
Week 6: Applications of Probability Models
- Queueing theory
- Reliability theory
- Finance
Common Mistakes to Avoid:
- Confusing probability with frequency
- Ignoring conditional probability
- Making assumptions about independence that are not justified
How to Approach the Course:
- Read the textbook before each lecture
- Attend all lectures and take notes
- Do the homework assignments on time
- Get help from the instructor or a tutor if needed
- Review the material regularly
Four Useful Tables
| Distribution | PMF/PDF | Mean | Variance |
|---|---|---|---|
| Bernoulli | P(X = x) = p^x (1-p)^(1-x) | p | p(1-p) |
| Binomial | P(X = x) = (n choose x) p^x (1-p)^(n-x) | n*p | np(1-p) |
| Poisson | P(X = x) = (e^(-lambda) * lambda^x) / x! | lambda | lambda |
| Normal | f(x) = (1 / (sigma * sqrt(2pi))) * exp(-(x-mu)^2 / (2sigma^2)) | mu | sigma^2 |
Creative New Word: Probality
Probality is a portmanteau of the words “probability” and “ability.” It can be used to generate ideas for new applications of probability models. For example, we could consider the probality of success for a new product launch. Or, we could consider the probality of failure for a new engineering design. By thinking in terms of probality, we can open up new possibilities for using probability models to solve real-world problems.
