Probability and statistics (for SV)

Professor: Mats J. Stensrud

Head assistant: Gellért Perényi 

Teaching methods

Lectures, where I will use a (digital) whiteboard, which will be auto updated on this website (but that sometimes takes a few days). The sessions will not be recorded. 

The TAs will respond to questions on Ed Discussion (see the link below), but generally we will not respond to emails. Thus, please use Ed Discussion for all questions about the course. 

Assessment methods

Final exam (100% of the total grade). 

Teaching resources

• This course builds on the material created by Joe Blitzstein, https://projects.iq.harvard.edu/stat110/home.
• In particular, this book is relevant.

Lecture notes

• The digital blackboard,
• which will be updated continuously and will be made available after each session. Let me know if you detect typos.

• All questions about the course and the material should be asked in lectures, in exercise sessions or on Ed Discussion.
• Emails will, broadly speaking, not be answered.

Main topics

1. Probability and counting

2. Conditional probability

3. Random variables and their distributions

4. Expectation

5. Continuous random variables

6. Moments

7. Joint distributions

8. Transformations

9. Conditional expectation

10. Inequalities and limit theorems

11. Basic statistics

12. Design of experiments

    
    

    
    

Introduction and structure of the course: 

• Structure of the course
• Broad advice

Probability and Counting:

• Why study probability?
• Sample spaces
• Naive and non-naive definitions of probability

The material I will cover can be found in Chapters 1.1-1.5 of the book, which also includes additional examples. 

Definitions of probability (continues) 

• Examples and intuition
• Properties of probability
• Inclusion-exclusion

Conditional probability

• Independence
• Bayes rule
• Examples

The material I will present is described in Chapters 1.6, 1.7, 2.1, 2.2 and the beginning of 2.3 of the book

Conditional probability

Independence (and thinking about uncertainty!)

Examples

Conditional independence

Monty Hall problem 

Simpson's paradox

The material can be found in the book chapters 2.3 - 2.7

Conditional probability (we will continue doing this important topic)

Random variables and their distributions (including Bernoulli and Binomial)

CDFs (Cumulative Distribution Functions)

PMFs (Probability Mass Functions) 

Hypergeometric distribution

Averages and expected values  

Indicator r.v.s

Linearity of expectation, symmetry

Fundamental bridge

Negative Binomial

The material can be found in the book chapters 4.1-4.4

Poisson distribution, Variance, Standard deviation, LOTUS

The material is found in Chapter 4.6 and 4.7. See also partly 4.8.

No teaching this week

Continuous Random Variables, Uniform Distribution, Normal distribution

The material can be found in Chapters 5.1-5.4.

Normal distribution (continuous), Note on Location-Scale shift, Standardization, transformations of RVs (LOTUS revisited), Exponentially distributed RVs, Summaries of distributions

Chapters 5.4, 5.5 , part of 5.7 and Chapter 6.1

Summaries of distributions, Joint distributions, conditional distributions, marginal distributions, 2D LOTUS, Covariance and Correlation

Chapters 6.1, 7.1 - 7.4

Conditional expectation and variance, Inequalities

9.4, 9.5, 9.6

10.1

Law of Large Numbers, Central Limit Theorem 

10.2 and 10.3

Introduction to Statistics (including the Salk trial) 

basic statistics, point estimation and confidence intervals


This is not discussed in the book. You will receive a separate copy of notes, that will be uploaded here

Mock exam during the lecture

Then we will go through the mock exam after the lecture