MATH 464/564 Probability II (Winter 2021)
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Meets: live via Zoom MWF 11:00 am - 11:50 am, or prerecorded.
Grading scheme: Homework 60%, Online quizzes 40%
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Textbooks:
(1) Charles M. Grinstead and J. Laurie Snell, Introduction to Probability available as a FREE e-book at http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
A hard copy of the textbook can be acquired at bookstores such as Amazon.
(2) Mark Huber, Probability: Lectures and Labs available as a FREE e-book at https://www.markhuberdatascience.org/probability-textbook
A hard copy of the textbook can be acquired at bookstores such as Amazon.
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Prerequisites: MTH 463/563 and MTH 341. A minimum grade of C- is required in MTH 463/563 and MTH 341.
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Syllabus: PDF file
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Homework: The homework assignments will need to be submitted in PDF format via Canvas and before the respective deadline. Late homework will not be accepted.
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Homework #1 (due Monday, January 25): HW 1 (PDF)
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Homework #2 (due Monday, February 8): HW 2 (PDF)
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Homework #3 (due Monday, February 22): HW 3 (PDF)
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Homework #4 (due Monday, March 8): HW 4 (PDF)
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Schedule:
Monday, January 4 Joint probability mass function. Joint probability density function. Independent random variables. Sums of random variables. Huber: Chapter 13 Lectures 1-6 slides (PDF)
Wednesday, January 6 Sums of random variables. Gamma and beta random variables. Examples. Grinstead and Snell: Sections 7.1 and 7.2 Huber: Chapter 13 Lectures 1-6 slides (PDF)
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Friday, January 8 Gamma and beta random variables. Poisson process. Grinstead and Snell: Sections 7.1 and 7.2 Huber: Chapters 13 and 21 Lectures 1-6 slides (PDF)
Monday, January 11 Poisson process. Marginal distributions from joint distribution. Grinstead and Snell: Sections 7.1 and 7.2 Huber: Chapters 13 and 21 Lectures 1-6 slides (PDF)
Wednesday, January 13 Marginal distributions from joint distribution. Expectations of functions of random variables. Grinstead and Snell: Sections 7.1 and 7.2 Huber: Chapters 13 and 23 Lectures 1-6 slides (PDF)
Friday, January 15 Covariance and correlation. Huber: Chapters 14 and 15 Lectures 1-6 slides (PDF)
Wednesday, January 20 Covariance and correlation. Multivariate normal distribution. Huber: Chapters 14, 15, and 16 Lectures 7-11 slides (PDF)
Firday, January 22 Covariance and correlation. Multivariate normal distribution. Huber: Chapters 15, 16, and 30 Lectures 7-11 slides (PDF)
Monday, January 25 Multivariate normal distribution. Huber: Chapter 30 Lectures 7-11 slides (PDF)
Friday, January 29 Multivariate normal distribution. Huber: Chapter 30 Lectures 7-11 slides (PDF)
Monday, February 1 Multivariate normal distribution. Indicator variables. Huber: Chapter 30 Lectures 7-11 slides (PDF)
Wednesday, February 3 Indicator variables. Conditional distributions. Huber: Chapter 12 Lectures 12-17 slides (PDF)
Friday, February 5 Conditional distributions. Conditional expectation. Huber: Chapters 12 and 24 Lectures 12-17 slides (PDF)
Monday, February 8 Conditional expectation. Wald's equation. Conditional variance. Huber: Chapters 12 and 24 Lectures 12-17 slides (PDF)
Wednesday, February 10 Conditional variance. The law of total variance. Variance of a random sum of random variables. Huber: Chapters 12 and 24 Lectures 12-17 slides (PDF)
Friday, February 12 Conditional expectation as a projection. The law of total variance via Pythagorean Theorem. Huber: Chapters 12 and 24 Lectures 12-17 slides (PDF)
Monday, February 15 Conditional distributions and randomization formulas. Moment generating functions. Huber: Chapters 12 and 17 Lectures 12-17 slides (PDF)
Wednesday, February 17 Moment generating functions. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapter 17 Lectures 18-24 slides (PDF)
Friday, February 19 Moment generating functions. Examples. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapter 17 Lectures 18-24 slides (PDF)
Monday, February 22 Moment generating functions. Proving de Moiver-Laplace Theorem via moment generating functions. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapter 17 Lectures 18-24 slides (PDF)
Wednesday, February 24 Proving Central Limit Theorem via moment generating functions. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapter 17 Lectures 18-24 slides (PDF)
Friday, February 26 Proving Central Limit Theorem via moment generating functions. Probabilistic inequalities. One-sided Chebyshev inequality. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapter 17 Lectures 18-24 slides (PDF)
Monday, March 1 Probabilistic inequalities. Chernoff bound. Characteristic functions. Generating functions. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapters 17, 25, and 26 Lectures 18-24 slides (PDF)
Wednesday, March 3 Chernoff bound. Jensen's inequality. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapters 17, 25, and 26 Lectures 18-24 slides (PDF)
Friday, March 5 Chernoff bound. Jensen's inequality. Characteristic functions. Generating functions. Grinstead and Snell: Sections 10.1 and 10.3 Huber: Chapters 17, 25, and 26 Lectures 25-28 slides (PDF)
Monday, March 8 Characteristic functions. Generating functions. Branching process. Grinstead and Snell: Chapter 10 Huber: Chapter 17 Lectures 25-28 slides (PDF)
Wednesday, March 10 Branching process. Grinstead and Snell: Chapter 10 Huber: Chapter 17 Lectures 25-28 slides (PDF)
Friday, March 12 Size biasing. Functions of random variables. Lectures 25-28 slides (PDF)