# Data 88S: Probability and Mathematical Statistics for Data Science

UC Berkeley, Spring 2024

## Week 9

- The homework that will cover this week’s material, Homework 8, has been released. It is due Tuesday, March 19, at 11:59PM.

# Calendar

## Week 1: The Fundamentals

- Jan 15
*Martin Luther King Jr. Holiday*- Jan 17
**Lecture**Probabilities as Proportions (Blank Slides)- Syllabus, Ch 1.1.1 - 1.1.5

**Homework**Homework 1- Due Jan 22 at 4PM

- Jan 19
**Section**Worksheet

## Week 2: Conditioning, Bayes Rule, Independence

- Jan 22
**Lecture**The axioms of probability (Blank Slides)- Ch 1.3

**Homework**Homework 2- Due Jan 29 at 4PM

- Jan 24
**Lecture**Conditioning, updating (Blank Slides)- Ch 2.1 - 2.3

**Section**Worksheet- Jan 26
**Lecture**Bayes’ examples, Independence (Blank Slides)- Ch 2.4, 2.5

**Section**Worksheet

## Week 3: Random Variables

- Jan 29
**Lecture**Examples of symmetry, Bayes’ theorem (Blank Slides)- Ch 3.1, 3.2

**Homework**Homework 3- Due Feb 5 at 4PM

- Jan 31
**Section**Worksheet- Feb 2
**Lecture**Random counts, binomial (Blank Slides)- Ch 3.3.4 - 3.3.6

**Quiz 1**

## Week 4: Random Counts

- Feb 5
**Lecture**Random counts, continued (Blank Slides)- Ch 3.4.1 - 3.4.4, 3.5

**Homework**Homework 4 (PDF)- Due Feb 13 at 11:59PM

- Feb 7
**Section**Worksheet- Feb 9
**Lecture**Exponential approximations (Blank Slides)- Ch 4.3.1 - 4.3.4

**Section**Worksheet

## Week 5: CDF continued

- Feb 12
**Lecture**Examples, CDF, Waiting Time (Blank Slides)- Ch 4.3.4, 4.4

**Homework**Homework 5- Due Feb 20 at 11:59PM

- Feb 14
**Lecture**Waiting Times (Blank Slides)- Ch 5.1, 5.2.1 - 5.2.4

**Section**Worksheet- Feb 16
**Lecture**Exponential Approximations (Blank Slides)- Ch 5.2.5 - 5.3

**Quiz 2**

## Week 6: The Poisson Distribution

- Feb 19
*President’s Day Holiday*- Feb 21
**Lecture**Poisson Distribution (Blank Slides)- Ch 5.4.1 - 5.4.7

**Section**Worksheet**Homework**Homework 6- Due Feb 27 at 11:59PM

- Feb 23
**Lecture**Expectation- Ch 5.5.1, 5.5.2, 5.5.3

**Section**Worksheet

## Week 7: Expectation and Variance

- Feb 26
**Lecture**Method of indicators, unbiased estimators- Ch 5.6.1 - 5.6.5

**Homework**Homework 7- Due Mar 6 at 11:59PM

- Feb 28
**Lecture**Conditional expectation, expectation by conditioning- Ch 6.1.1 - 6.1.4, 6.2.1, 6.2.2

**Section**Worksheet- Mar 1
**Lecture**Variance, standard deviation- Ch 6.3, 6.4

**Section**Worksheet

## Week 8: Additivity and Midterm

- Mar 4
**Lecture**Tail Bounds- Ch 7.1.1 - 7.1.4

- Mar 6
**Lecture**Additivity, Review (go over practice midterm)**Section**- Mar 8
**Midterm**

## Week 9: Conditional Expectation

- Mar 11
**Homework**Homework 8- Due Mar 19 at 11:59PM

- Mar 13
**Lecture**Variance + Standard deviation- Ch 7.3.1 - 7.3.6

**Section**Worksheet- Mar 15
**Lecture**Markov’s inequality- Ch 8.1 - 8.4

**Section**Worksheet

## Week 10: Confidence intervals, hypothesis testing, and density

- Mar 18
**Lecture**Confidence Intervals- Ch 9.1, 9.2

**Homework**- Mar 20
**Lecture**Testing hypotheses- Ch 9.3, 9.4

**Quiz 3**- Mar 22
**Lecture**Probability density- Ch 10.1.1 - 10.1.6

## Week 11: Spring Break

- Mar 25
*Spring Break*- Mar 27
*Spring Break*- Mar 29
*Spring Break*

## The law of averages, distribution of a sample sum

- Apr 1
**Homework**Homework 9- Due Apr 9 at 11:59PM

- Apr 3
**Section**Worksheet- Apr 5
**Lecture**The central limit theorem- Ch 8.3

**Section**Worksheet

## Week 13: Confidence Intervals

- Apr 8
**Lecture**Confidence Intervals (Blank Slides)- Ch 9.1-9.2

**Homework**Homework 10- Due Apr 16 at 11:59PM

- Apr 10
**Lecture**Confidence Intervals (Blank Slides)- Ch 9.1-9.2

**Section**Worksheet- Apr 12
**Lecture**A/B Testing and Confidence Intervals- Ch 9.3-9.4

**Quiz 4**

## Week 14: Density

- Apr 15
**Lecture**A/B Testing- Ch 9.3-9.4

**Homework**Homework 11- Due Apr 23 at 11:59PM

- Apr 17
**Lecture**Probability density- Ch 10.4

**Section**Worksheet- Apr 19
**Lecture**Probability density- Ch 10.4

**Section**Worksheet

## Week 15: Inference and Conclusion

- Apr 22
**Lecture**MSE and the regression equation- Ch 11.3, 11.4, 11.5

**Homework**Homework 12- Due Apr 30 at 11:59PM

- Apr 24
**Lecture**Residuals, SLR- Ch 11.5, 12.1

**Section**- Apr 19
**Lecture**Finishing up regression and correlation- Ch 12.1, 12.2 (12.3 if time)

**Section**

## Week 16: RRR Week

- Apr 29
*RRR Week*- May 1
*RRR Week*- May 3
*RRR Week*

## Week 17: Finals Week

- May 10
**Final Exam**- 8-11AM