MAT 135A: Probability (Fall 2017)
Course materials
All files are in the pdf format, which require the
free
Adobe Acrobat reader.
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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.
Problem 2(d): change "first four" to "first three" in the statement (or add
a factor of 10/49 in the solution).
Go to the
resources page for more sample exams.
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Standard Normal table and
Normal distribution calculator from Hyperstat.
- Matlab script that simulates relative
frequency of wins in De Mere games.
- Matlab script that computes the
probability of multiple birthdays.
- Matlab script that computes the probability
that all birthdays are represented by inclusion-exclusion.
- Matlab script that computes the probability
that all birthdays are represented by a recursive formula.
- World series
winning probabilities from
Society for American Baseball Research.
- Midterm 1 will be on Fri., Oct. 27, 2017, 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, the two Bayes' formulas, and independence.
The exam will be based on what we covered in class, so you should understand all examples
given in class even if they are not in the notes. For practice, solve
the Practice Exam 1 (in the Lecture Notes) on your own, then look at the solutions and solve it again.
Then do the same with the Sample Midterm 1 above. 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.
Calculations of expectation and variance of geometric distribution.
- Midterm 2 will be on Fri., Dec. 1, 2017, in class. It covers
Chapters 5-7 in the lecture notes, and homework assignments 4-6.
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. 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 even if they are not in the notes. For practice, solve
the Practice Exam 2 (in the Lecture Notes) on your own, then look at the solutions and solve it again.
Then do the same with the Sample Midterm 2 above.
The table for computing Φ(x), for x>0, will
be provided.
Solutions to Midterm 2.
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Finals Week Info