Announcements! ( See All )
4/28 - Final Assessment Part I has been released, and is due Tue 5/5 at 12PM noon.
4/21 - Week 13 Checkpoint, HW 12, and Lab 9 have been released. Week 13 Checkpoint is due Thu 4/23, HW 12 is due Tue 4/28, and Lab 9 is due Sun 5/3.
4/14 - Week 12 Checkpoint and HW11 have been released. Week 12 Checkpoint is due is due Thu 4/16, and HW 11 is due Tue 4/21
4/7 - Week 11 Checkpoint, HW 10, and Lab 8 have been released. Week 11 Checkpoint is due Thu 4/9, HW 10 is due Tue 4/14, and Lab 8 is due Sun 4/19.
3/31 - Homework 9 and the Week 10 Checkpoint have been released. Week 10 Checkpoint is due 4/2 and Homework 9 is due 4/7.
3/20 - Homework 8 and Lab 7 have been released. Homework 8 is due Tue 3/31 and Lab 7 is due Sun 4/5.
3/10 - Homework 7 and Lab 6 have been released. Homework 7 is due Tue 3/17 and Lab 6 is due Sun 3/15.
3/5 - Homework 6 has been released, and is due Tue 3/10. No Lab this week.
2/25 - Lab 5 has been released, and is due Sun 3/1. No Homework this week so you have time to study for the Midterm on Tue 3/3.
2/18 - Homework 5 has been released, and is due Tue 2/25. Lab 4 is due Sun 2/23.
2/11 - Homework 4 and Lab 4 have been posted! Lab 4 is due Sun 2/23. This is a challenging lab; please start early. Lab Party on Thu 2/13 is being converted to a Homework Party.
1/21 - Homework 1 and Lab 1 have been posted! First section Wed 1/22, please be sure to bring a laptop!

# Material for Final Exam

## General Concepts and Methods

### Probability

• Chapter 1: Spaces, events, basic counting, exponential approximation
• Chapter 2, Lab 1: 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: CDF and inverse CDF
• Chapter 16, Lab 7: Density of a transformation
• Chapter 17, Lab 7: 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 19.2: Moment generating function

### 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 6: 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, 25.4: 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 1: Hypergeometric
• Section 6.4, 6.5, Chapter 7, Sections 8.1, 8.3, 12.1, 19.2 and related homework, Lab 8: Poisson
• Sections 8.1, 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 20, 21: Relation with binomial

### 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 9: 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 8: Waiting times in a Poisson process

### Omitted from Both Parts I and II

• Chapters 10, 11
• Section 12.4
• Sections 14.1, 14.2 (everything to do with probability generating functions is omitted, but the general formula for the distribution of the sum at the start of Section 14.1 is not omitted)
• In Section 18.1, the derivation of the constant of integration is omitted but the rest is not omitted
• In Section 19.3, the “proof” of the Central Limit Theorem is omitted
• In Section 21.2, the general form of the beta-binomial distribution is omitted, but the expectation is not omitted
• Section 21.3
• In Section 24.1, the geometry of correlation as a cosine is omitted, but the rest is not omitted
• Section 25.1, 25.2

### Omitted from Part I but not from Part II

• Sections 25.3, 25.4