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

UC Berkeley, Summer 2023

## Week 8

- The homework on last week’s material, Homework 7 is due Monday, August 7th, at 11:59 PM. There are NO extensions on Homework 7.
- The final is on Thursday, August 10th at 10:30AM - 1:30PM in McCone 141. It will cover Chapters 1 through 11. Please see #126 on Ed.

# Calendar

## Week 1: The Fundamentals

- Jun 19
*Juneteenth Holiday*- Jun 20
**Section 1**- Ch 1 Ex 1, 3, 5, 2, 4

- Jun 21
- Jun 22
**Lecture 3**Updating chances; independence- Ch 2.3 - 2.5

**Section 2**- Ch 2 Ex 7, 5, 10, 4, 11, 6

## Week 2: Random Variables and Random Counts

- Jun 26
**Lecture 4**Random variables- Ch 3.1 - 3.2

- Jun 27
**Lecture 5**Random counts: binomial- Ch 3.3

**Section 3**- Ch 3 Ex 1, 2, 7, 9, 3, 8

- Jun 28
**Lecture 6**Random counts: hypergeometric- Ch 3.4 - 3.5

- Jun 29
**Lecture 7**Exponential approximations; geometric- Ch 4.1 - 4.3

**Section 4**- Ch 3 Ex 6, 10; Ch 4, Ex 4, 6, 5

## Week 3: The Poisson Distribution and Expectation

- Jul 3
**Lecture 8**Law of small numbers; Poisson- Ch 4.4

- Jul 4
*Independence Day Holiday*- Jul 5
**Lecture 9**Expectation and additivity- Ch 5.1 - 5.3

- Jul 6
**Lecture 10**Unbiased estimators- Ch 5.4

**Section 5**- Ch 4, Ex 7c, 6; Ch 5, Ex 4, 6, 9, 11, 7

## Week 4: Conditioning and Variance

- Jul 10
**Lecture 11**Expectation by conditioning- Ch 5.5 - 5.6

- Jul 11
**Lecture 12**Standard deviation; tail bounds- Ch 6.1 - 6.4

**Section 6**- Ch 5, Ex 13, 14, 15; Ch 6, Ex 2, 4, 7, 5

- Jul 12
**Lecture 13**Variance and additivity: binomial and hypergeometric- Ch 7.1 - 7.2

- Jul 13
**Lecture 14**Large samples: law of large numbers- Ch 7.3

**Section 7**- Ch 7, Ex 1, 3, 9, 4, 8; Law of Averages Question (not in textbook)

## Week 5: The Central Limit Theorem, Hypothesis Testing, and Densities

- Jul 17
**Lecture 15**Central Limit Theorem- Ch 8.1 - 8.4

- Jul 18
**Lecture 16**Confidence intervals- Ch 9.1 - 9.2

**Section 8**- Ch 8, Ex 1, 2, 3, 4; Ch 9, Ex 1, 2, 4

- Jul 19
**Lecture 17**Testing hypotheses- Ch 9.3 - 9.4

- Jul 20
**Lecture 18**Probability density- Ch 10.1

**Section 9**- Ch 9, Ex 5, 9, 7, 8, 10; Integration Practice (not in textbook)

## Week 6: Densities and Estimation

- Jul 24
**Lecture 19**Expectation and variance revisited- Ch 10.2

- Jul 25
**Lecture 20**The exponential distribution- Ch 10.3

**Section 10**- Ch 10, Ex 1, 2, 10, 3, 4

- Jul 26
**Lecture 21**The normal distribution- Ch 10.4

- Jul 27
**Lecture 22**Estimation: bias and variance- Ch 11.1 - 11.2

**Section 11**- Ch 10, Ex 7, 8, 5, 9, Ch 11, Ex 1, 2

## Week 7: Regression

- Jul 31
**Lecture 23**Correlation and the regression line; the regression effect- Ch 11.3 - 11.4

- Aug 1
**Lecture 24**Error in regression- Ch 11.5

**Section 12**- Ch 11, Ex 3, 4, 9, 11, 10, 7

- Aug 2
**Lecture 25**Inference in regression- Ch 12.1 - 12.3

- Aug 3
**Lecture 26**Conclusion**Quiz 6**- Ch 10

**Section 13**- Ch 12, Ex 3, 4

## Week 8: Review and Final Exam

- Aug 7
**Lecture 27**Buffer/Review- Aug 8
**Lecture 28**Buffer/Review**Section 14**- Practice Problems 10, 21, 22, 25, 18, 14, 13

- Aug 9
**Lecture 29**Buffer/Review- Aug 10
**Final Exam**From 10:30 AM - 1:30 PM