MAT 135A: Probability (Fall 2025)
Course materials
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Complete lecture notes. Please let me know of any mistakes.
You will receive extra credit commensurate with the resulting improvements.
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Sample Midterm 1.
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Sample Midterm 2.
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Sample Final.
Go to the
resources page for more sample exams.
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Homework Assignment 1.
Due, but not collected, on Tue., Oct. 7.
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Homework Assignment 2.
Due, but not collected, on Tue., Oct. 14.
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Homework Assignment 3.
Due, but not collected, on Tue., Oct. 21.
- Midterm 1 will be on Fri., Oct. 24, 2025, in class. It covers the
first four chapters of Lecture Notes, and
first three homework assignments. Topics: combinatorial probability
(permutations, combinations), consequences of the axioms (inclusion-exclusion),
conditional probability, conditioning and Bayes' formulas, and independence.
The exam will be based on what we covered in class, so you should understand all examples
given in class and in the discussion. For practice, solve
the latest Sample Midterm 1, then look at the solutions and solve it again. For more practice, there are several
more past Midterm 1 exams on the
resources page and
the Practice Midterm 1 on pages 39-44 of the Lecture Notes.
Homework problems are also good practice. You will not be able to ask interpretation
questions during exams; proper interpretation of word problems is part of the exam.
Solutions to Midterm 1.
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Homework Assignment 4.
Due, but not collected, on Tue., Oct. 28.
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Homework Assignment 5.
Due, but not collected, on Tue., Nov. 4
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Standard Normal table and
Normal distribution calculator from Hyperstat.
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Homework Assignment 6.
Due, but not collected, on Tue., Nov. 11
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Homework Assignment 7.
Due, but not collected, on Tue., Nov. 18
- Midterm 2 will be on Fri., Nov. 21, 2025, in class. It covers
Chapters 5-7 in the lecture notes, and homework assignments 4-7.
Topics: discrete random variables
(probability mass function, expectation, variance, binomial, Poisson, geometric), approximation of binomial
with Poisson,
continuous random variables (density, expectation, variance,
distribution of a function, uniform, exponential, normal), approximation
of binomial with normal,
joint distributions and independence. Conditional distributions
(last part of Chapter 7) will not be on this exam.
The exam will be based on what we covered in class, so you should understand all examples
given in class and in the discussion. For practice, solve
the latest Sample Midterm 2,
then look at the solutions and solve it again. For more practice, there are several
more past Midterm 2 exams on the
resources page and
the Practice Midterm 2 on pages 81-86 of the Lecture Notes.
Homework problems are also good practice. As on all exams, you will not be able to ask interpretation
questions during exams; proper interpretation of word problems is part of the exam. You will not need to compute Φ(x);
you can leave any expression of the form Φ(x), for x>0,
unevaluated in your answers.
Solutions to Midterm 2. (Note. There was a misprint in 3(b), as 5·9·9+15 =240 not 190. Full credit was given both for using 190 and for using 5·5·9+15.)
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Homework Assignment 8.
Due, but not collected, on the last day of classes
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Finals Week Info
Solutions to Final Exam.