### MAT 135A: Probability (Fall 2017) Course materials

All files are in the pdf format, which require the free Adobe Acrobat reader.
• Complete lecture notes. Please let me know of any mistakes. You will receive extra credit commensurate with the resulting improvements.
• Sample Midterm 1.
• Sample Midterm 2.
• 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.
• 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.

• Finals Week Info