Introduction to Probability Theory

Homework will be assigned (every one or two weeks) and collected, but it will **not** be graded. Nominal credit will be given for submitting your solutions for the homework problems (10% of the course grade for submitting all homework sets). **You must submit your homework to your TA either during your discussion section or in one of their office hours.** Detailed solutions to several homework exercises will be given during the discussion sections and, for some problems, during the lectures. Working on the homework problems will enable you to develop facility in probabilistic thinking through regular practice. Moreover, it will provide early and regular feedback on your performance in the course through the solutions discussed during the sections, lectures, and office hours. Please plan to work consistently throughout the quarter on the homework problems, attempting to solve them **before** they are discussed in sections or class. The capacity to independently solve homework problems is a strong predictor for good performance in the exams.

**Homework 1 (due by Friday 10/12)**

Section 1.4: Exercises 5, 6, 7, 8

Section 1.5: Exercises 3, 4, 9, 11, 12, 13

Section 1.6: Exercises 1, 3, 4, 8

Section 1.7: Exercises 5, 6, 7, 8, 9

**Homework 2 (due by Tuesday 10/30)**

Section 1.8: Exercises 7, 8, 11, 13, 18

Section 1.9: Exercises 3, 7, 8

Section 1.10: Exercises 2, 3

Section 2.1: Exercises 4, 5, 10, 13, 14

Section 2.2: Exercises 2, 5, 7, 10, 13, 15, 23 (for problems 13 and 15, assume that particles are emitted independently)

Section 2.3: Exercises 5, 7, 8, 9, 12, 13, 14 (for problems 7 and 8, assume conditional independence for successive tosses given the type of coin)

**Homework 3 (due by Wednesday 11/14)**

Section 3.1: Exercises 2, 5, 8, 10

Section 3.2: Exercises 3, 5, 6, 10, 11

Section 3.3: Exercises 4, 5, 8, 11, 13

[Answers for exercise 3.3.4: (a) 0.1; (b) 0.1; (c) 0.2; (d) 0; (e) 0.6; (f) 0.4; (g) 0.7; (h) 0; (i) 0; (j) 0; (k) 0; (l) 0.2]

Section 3.4: Exercises 2, 3, 5, 7, 10

**Homework 4 (due by Tuesday 11/27)**

Section 3.5: Exercises 2, 5, 7, 8, 11

Section 3.6: Exercises 1, 2, 7, 8, 9, 12

Section 3.8: Exercises 2, 3, 4, 8, 13

Section 3.9: Exercises 1, 2, 7, 8

**Homework 5 (due by Monday 12/10, before the beginning of the final exam)**

Section 4.1: 4, 8, 9

Section 4.2: 3, 4, 6, 7

Section 4.3: 2, 3, 5, 12