Math 416: Probability


Course Information

Professor: Kiril Datchev
Email: kdatchev@purdue.edu
Lectures: Tuesdays and Thursdays, 12:00 to 1:15, in SCHM 113.
Textbook: A First Course in Probability, 10th edition, by Sheldon Ross, ISBN 9780134753119.
Office hours: after class, Wednesdays 1-2, or by appointment, in MATH 602.
Help room schedule in MATH 205/211: Mondays 3:30-4:30, Tuesdays 12-4, Wednesdays 10-12 and 3:30-4:30, Thursdays 12-4, and Fridays 2:30-3:30.

We will cover the following topics: general probability rules, conditional probability and Bayes theorem, discrete and continuous random variables, moments and moment generating functions, joint and conditional distributions, standard discrete and continuous distributions and their properties, law of large numbers and central limit theorem.

Grading is based on
  • Almost weekly homework assignments, worth 20% of the total grade,
  • two in-class midterm exams, one on September 30th and one on November 4th, each worth 20% of the total grade,
  • a final exam, as scheduled here, worth 40% of the total grade.

    • Homework

    Homework is due on paper at the beginning of class on Thursdays. Justify your answers. Here are the assignments:

    Homework 1, due September 4th, is Chapter 1, Problems 1, 3, 10, 23, 24, 26, 30, 34, Theoretical Exercises 8, 9, 10, 13.

    Homework 2, due September 11th, is Chapter 2, Problems 6, 10, 18, 20, 25 (for this one, solve it at least two ways and check that the answers agree: one by following the hint and one by computing the chances of getting 5 on a roll that is a 5 or a 7) 28, Theoretical Exercises 5, 6adi, 7a.

    Homework 3, due September 18th, is Chapter 2, Problems 34, 37, 54, Theoretical Exercises 11, 13, 12 (use 13 for 12) , Chapter 3, Problems 10, 11, 13, Theoretical Exercises 2, 5a.

    Review problems for Midterm 1.

    Homework 4, due October 9th, is Chapter 3, Problems 23, 26, 30, Theoretical Exercise 11, Chapter 4, Problems 6, 7, 11, 22a, 26 (for 26, also find each variance), 39, Theoretical Exercise 4.

    Homework 5, due October 16th, is Chapter 3, Problems 50, 60, 64, 89, Chapter 4, Problems 44, 50, 54, 61 (for part b, where the approximation is bad, also get a better approximation by switching the roles of success and failure to convert to a problem where p and k are small), Theoretical Exercises 11 (Hint: show that P(X=n+1)/P(X=n) < 1 by simplifying the fraction and using 2n+1<2n+2 and p(1-p)) ≤ 1/4), 18b.

    Homework 6, due October 23rd, is Chapter 4, Problem 69, Theoretical Exercise 19, Chapter 5, Problems 4a, 7, 11, 15ab, 16, 18, 22, 25, 26, 28.

    Review problems for Midterm 2.


    Additional Materials

    Paul's Notes for the prerequisites.

    A philosophical essay on probabilities by Laplace for probability in a broader context.



    A list of general policies and procedures can be found here.