Course taught by Prof. Sotos.
Textbooks
- https://utstat.utoronto.ca/mikevans/jeffrosenthal/
- https://drive.google.com/file/d/1VmkAAGOYCTORq1wxSQqy255qLJjTNvBI/edit
Notes
- Take-home quizes
- Office hours TUES, THURS 1-3pm IA4072
- 15% quiz best 9/11
- Term test 1 20% (Week 1-4)
- Formula sheet will be handed out
- A tiny bit of expectations questions
- Term test 2 20% (Week 5-8)
- Final 45%
- Problem-set and solution set will be posted each week
Concepts
Week 1
- Probability Model
- Naive Set Theory
- Probability
- Experiment
- Outcome
- Sample Space
- Event
- Tuple
- Venn Diagrams
- Union Notation
- Intersection Notation
- Probability Function
- Probability Axioms
- Probability Rules
- Subset
- Disjoint
- Partition
- Discrete Sample Space
- Discrete Uniform Probability Space
- Counting
- Partial Derivative
- Jacobian Matrix
- Multiple Integral
- Change of Order of Integration
- Change of Integration Variables
Week 2
- Conditional Probability
- Bayesian Statistics
- Conditional Probability Axioms
- Regular Probability Theorem
- Bayes Theorem
- Prevalence of Condition
- Finding Unconditional Probability from Conditional Probabilities Example
- Multinomial Coefficient
- Multinomial Distribution
- Independent Events
- Mutual Independence
- Conditioning on Multiple Events
- Pairwise Independence Does Not Imply Mutual Independence
- Multiplication Rule of Probability
- Conditional Independence
Week 3
- Random Variable
- Probability Distribution
- Functions of Random Variables
- Probability Mass Function
- Probability Density Function
- Cumulative Distribution Function
- PMF From CDF
- PDF From CDF
- CDF and PDF Example
- Bernoulli Random Variables
- Bernoulli Distribution
- Binomial Random Variable
- Binomial Distribution
- Binomial Theorem
- Hypergeometric Distribution
Week 4
- Expectation
- Geometric Distribution
- Geometric Series
- Negative Binomial Distribution
- Poisson Distribution
- Variance
- Urn Problem
- Binomial Formulas
Week 5
- Continuous Random Variable
- PDF From CDF
- Uniform Continuous Probability Distribution
- Exponential Continuous Probability Distribution
- Expected Value of Continuous RV
- Gamma Distribution
- Normal Distribution
Week 6
- Multivariate Distribution
- Joint Probability Mass Function
- Joint Cumulative Distribution Function
- Joint PMF to Marginal PMF
- Multinomial Coefficient
- Multinomial Theorem
- Joint CDF to Marginal CDF
- Joint Probability Density Function
- Joint CDF to Joint PDF
- Joint PDF to Marginal PDF
- Expected Value of Discrete Multiple RV
- Expected Value of Continuous Multiple RV
- Bivariate Normal
- Weibull Distribution
- Hazard Rate
Week 7
- Conditional Probability Mass Function
- Conditional Probability Density Function
- Conditional Cumulative Density Function
- Independent Random Variable
Week 8
- Functions of Random Variables
- Deriving Distribution for Transformation
- Probability Simulation
- Functions of Multiple Random Variables
- Deriving Distribution for Multivariable Transformation
- Order Statistics
- IID
- Distribution of Maximum Order Statistic
- Distribution of Minimum Order Statistic
- Sum of Random Variables
Week 9
- Covariance
- Correlation
- Random Variable Linear Dependence
- Conditional Expectation
- LoTE
- Law of Total Variance
- Bivariate Normal
Week 10
- Moment
- Central Moment
- Moment Generating Function
- MGF Method
- Moment Generating Function Factorization Method
- Markov Inequality
- Chebyshev Inequality
- Jensen Inequality
- Cauchy Schwarz Inequality Expectation
Week 11
- Average of Random Variable
- Weak Law of Large Numbers
- Probability Convergence
- Distribution Convergence
- Standardized Average
- Central Limit Theorem