Announcements! ( See All )
5/4 - Final exam study resources posted! Please see Piazza for updated OH schedule.
4/30 - Homework 13 has been posted! Due Sun 5/5 at noon. No supplementary sections on Fri 5/3.
4/23 - Week 14 assignments have been posted!
4/16 - Week 13 assignments have been posted! Quiz 4 will be on Wed 4/24 in section.
4/9 - Week 12 assignments have been posted!
4/2 - Homework 9 has been posted! Quiz 3 will be on Wed 4/10 in section.
3/19 - Week 9 assignments have been posted! Lab 8 due Sun 3/24 at noon. HW 8 due Tue 4/2 at noon.
3/12 - Week 8 assignments have been posted! Quiz 2 will be on Wed 3/20 in section.
3/5 - Week 7 assignments have been posted!
2/19 - Week 5 assignments have been posted! Midterm 1 on Thu 2/28.
2/12 - Week 4 assignments have been posted! Lab 4 due on Sun 2/17 at noon.
2/5 - Week 3 assignments have been posted! Quiz 1 on Wed 2/6 in your assigned section.
1/29 - Week 2 assignments have been posted! Quiz 1 will be on Wed 2/6 in section.
1/22 - Week 1 assignments have been posted! Please bring your laptops to section.

Material for Final Exam

General Concepts and Methods

Probability

• Chapter 1, Lab 1: Spaces, events, basic counting, exponential approximation
• Chapter 2: Addition and multiplication rules; conditioning and updating
• Chapter 5: Unions and intersections of several events
• Section 9.1: Probabilities by conditioning and recursion (discrete)
• Section 20.2: Probabilities by conditioning on a continuous variable
• Sections 4.5, 20.3: Independence

Distribution

• Chapter 3: Intro; equality versus equality in distribution
• Chapter 4: Joint, marginals, conditionals, independence (discrete case)
• Sections 5.3, 5.4: Random permutations and symmetry
• Sections 15.1, 15.2: Density
• Section 15.1 and Lab 7: CDF and inverse CDF
• Chapter 16, Lab 8: Density of a transformation
• Chapter 17, Lab 8: Joint, marginal, and conditional densities; independence
• Chapters 14, 19: Distribution of sum
• Section 14.3, 14.4, 15.3, 19.3: Central Limit Theorem

Expectation

• Chapter 8: The crucial properties (discrete case) including method of indicators and expectations of functions
• Lab 3: Tail sum formula and applications; see also geometric distribution
• Section 12.3, 19.4: Bounds: Markov, Chebyshev, Chernoff
• Section 9.2, 9.3: Expectation by conditioning
• Section 15.3, 17.1: Expectation using densities and joint densities
• Section 14.1, 14.2, 21.2: Generating functions

Variance

• Chapter 12: Intro, linear transformations
• Chapter 13: Covariance; variance of a sum
• Lab 6: Application of mean and variance of simple random sample sum
• Homework 11: Correlation and its properties
• Sections 22.2, 22.3: Variance by conditioning, mixtures
• Sections 23.1, 25.1: Mean and covariance for random vectors

Estimation and Prediction

• Section 8.2: Unbiased estimates
• Sections 14.4, 14.5: IID sample mean; confidence interval for population mean
• Section 20.1: Maximum likelihood estimate
• Section 20.2: Posterior density, MAP estimate
• Sections 12.2, 22.1, 22.4: Expectation and conditional expectation as least squares predictors
• Sections 24.2, 25.2: Least squares linear predictor

Special Distributions

Random Counts

• Sections 8.1, 12.1: Uniform on 1, 2, …, n
• Sections 6.1, 6.2, Chapter 7, 13.2, 14.3, Chapter 21: Bernoulli, binomial and multinomial
• Sections 6.3, 8.2, 13.3, 13.4, Lab 2: Hypergeometric
• Section 6.4, 6.5, Chapter 7, Sections 8.1, 8.3, 12.1, 19.2 and related homework, Lab 9: Poisson
• Homework 3, Lab 4, Lab 9, Sections 9.3, 22.3: Geometric

Uniform $(a, b)$

• Section 15.3, 19.1: Density, expectation, variance, CDF, density of sum

Beta

• Section 17.4: Integer parameters; uniform order statistics
• Chapter 21: Relation with binomial; beta-binomial distribution

Normal

• Section 14.3: CLT
• Sections 14.4, 14.5: Normal confidence intervals
• Section 16.1: Normal densities
• Sections 18.1, 18.2, 18.4: Independent normal variables, linear combinations, squares, Rayleigh, chi squared
• Section 19.3: Normal MGF, sums, CLT
• Chapter 24, Lab 11: Bivariate normal, linear combinations, independence, regression
• Chapters 23, 25: Multivariate normal, linear combinations, independence, regression

Gamma

• Section 15.4: Exponential
• Homework 8: Gamma function, gamma density, mean, variance
• Sections 18.3, 18.4: Gamma and chi squared
• Sections 19.2: Sums of independent gammas with the same rate
• Lab 9: Waiting times in a Poisson process

Omitted from Final

• Chapters 10, 11
• Section 12.4
• Section 25.1, 25.2