Data 88S: Probability and Mathematical Statistics for Data Science

UC Berkeley, Spring 2025

Week 4

Feb 11

Homework 4 has been released. It is due next Tuesday, February 18th at 5 PM.

Calendar

Jump to current week

Week 1: Fundamentals

Jan 20

Martin Luther King Jr. Holiday

Jan 22

Lecture Course introduction; fundamentals: Syllabus, Ch 1.1

Section No Section

Homework Homework 1: Due Jan 28 at 5PM

Jan 24

Lecture Exact calculations, and bounds: Ch 1.2-1.3

Section Ch 1 Ex 1, 2, 5

Week 2: Conditioning, Bayes Rule, Independence

Jan 27

Lecture Intersections of several events: Ch 2.1-2.2

Jan 28

Homework Homework 2: Due Feb 4 at 5PM

Jan 29

Lecture Updating chances: Bayes’ rule: Ch 2.3-2.4

Section Ch 2 Ex 5, 10, 6

Jan 31

Lecture Bayes’ rule examples, independence: Ch 2.4-2.5

Section Ch 2 Ex 11, 12, 4

Week 3: Random Variables

Feb 3

Lecture Random variables: Ch 3.1-3.2

Feb 4

Homework Homework 3: Due Feb 11 at 5PM

Feb 5

Lecture Random variables and their distributions: Ch 3.2

Section Ch 3 Ex 1, 8, 7

Feb 7

Lecture Random counts: the binomial: Ch 3.3

Section Ch 3 Ex 2, 9, 3

Week 4: Random Counts

Feb 10

Lecture Random counts: the hypergeometric: Ch 3.4

Feb 11

Homework Homework 4: Due Feb 18 at 5PM

Feb 12

Lecture CDF; waiting times: Ch 4.1-4.2

Section Ch 3 Ex 6, 10, Ch 4 Ex 2

Feb 14

Lecture Waiting times; exponential approximation: Ch 4.2-4.3

Section Ch 4 Ex 4, 5, 6

Week 5: Random Counts; Expectation

Feb 17

President’s Day Holiday

Feb 19

Lecture The Poisson distribution: Ch 4.4

Section Ch 4 Ex 7, 8, 12

Feb 21

Lecture Expectation: Ch 5.1

Section Ch 5 Ex 1a, 2 Midterm Review Problems

Week 6: Midterm; Expectation

Feb 24

Lecture Midterm review

Feb 26

Exam Midterm 1: 12PM - 1PM

Feb 28

Lecture Functions of random variables; additivity: Ch 5.2

Section

Week 7: Expectation

Mar 3

Lecture Method of indicators: Ch 5.3

Mar 5

Lecture Unbiased estimators: Ch 5.4

Section

Mar 7

Lecture Conditional distribution and expectation: Ch 5.5

Section

Week 8: Variance & SD

Mar 10

Lecture Expectation by conditioning: Ch 5.6

Mar 12

Lecture Measuring variability: Ch 6.1-6.2

Section

Mar 14

Lecture Tails of distributions: Ch 6.3-6.4

Section

Week 9: Variance of a Sum

Mar 17

Lecture Variability of a random sample sum: Ch 7.1

Mar 19

Lecture The accuracy of a simple random sample: Ch 7.2

Section

Mar 21

Lecture Large samples and the law of averages: Ch 7.3

Section

Week 10: Spring Break

Mar 24: Spring Break
Mar 26: Spring Break
Mar 28: Spring Break

Week 11: Central Limit Theorem

Mar 31

Lecture Central Limit Theorem 1: Ch 8.1-8.2

Apr 2

Lecture Central Limit Theorem 2: Ch 8.2-8.3

Section

Apr 4

Lecture Inference: confidence intervals based on the CLT: Ch 9.1-9.2

Section

Week 12: Midterm; Inference

Apr 7

Lecture Midterm review

Apr 9

Exam Midterm 2: 12PM - 1PM

Apr 11

Lecture Inference: testing hypotheses 1: Ch 9.3

Section

Week 13: Inference; Density

Apr 14

Lecture Inference: testing hypotheses 2: Ch 9.4

Apr 16

Lecture Probability density: Ch 10.1

Section

Apr 18

Lecture Expectation and variance; the uniform distribution: Ch 10.2

Section

Week 14: Density; Estimation

Apr 21

Lecture The exponential distribution: Ch 10.3

Apr 23

Lecture Some properties of the normal distribution: Ch 10.4

Section

Apr 25

Lecture Estimator: bias and variance: Ch 11.1

Section

Week 15: Regression

Apr 28

Lecture The regression line: Ch 11.3

Apr 30

Lecture Correlation: Ch 11.3-11.4

Section

May 2

Lecture The error in regression: Ch 11.5

Section

Week 16: RRR Week

May 5: RRR Week
May 7: RRR Week
May 9: RRR Week

Week 17: Finals Week

May 14

Final Exam: 3PM - 6PM