Note that doing only the Homework examples is likely insufficient to gain practice and understanding. One learns by doing examples: this is true of all Math, but especially true of Probability. Examples other than the homework may be (?) suggested on the schedule. The TA, Nick Basch will be doing many examples with you; usually in the Monday class.
Note also the information regarding homeworks on the
Class home page.
Homeworks are only final at 11.30 a.m. on Wednesdays, ONE WEEK before homework is due. Up to that time, changes may be made. After that time, only ESSENTIAL changes will be made, and every effort will be made to inform students, usually via the class email.
Homework 1; Due 11.30 a.m. Wed October 7
Kelly: 1.1.4, 1.1.7, 1.1.8, 1.1.9, 2.1.7, 2.1.8
Homework 2; Due 11.30 a.m. Wed October 14
Kelly: 2.1.5, 2.1.12, 2.1.15, 2.1.16, 2.2.1, 2.2.3
Homework 3; Due 11.30 a.m. Wed October 21
Kelly: 2.2.7* and 2.4.7*, 2.2.13, 2.2.14, 2.3.1, 2.3.8, 2.4.1
*: These two one-liners count together as one question.
Homework 4; Due 11.30 a.m. Wed October 28
Kelly: 1.2.4 (a,b,c), 1.2.5, 1.2.8 (a,b,c), 1.2.10, 1.3.1 (a,b,c), 1.3.14
Note: 1.2.4, 1.2.8 and 1.3.1; do parts (a),(b), (c) only:
In 1.2.4: If you use the formula 1.2.7 as
Kelly suggests, you must show you understand how that formula comes about.
Homework 5; Due 11.30 a.m. Wed November 4
Kelly: 1.Supp.7, 3.1.7, 3.1.8, 3.2.3, 3.2.7, 3.3.7(c),(d).
1.Supp.7: this means the Supplementary Chapter 1 Exercises.
3.3.7(c),(d): Note (c) (d) only -- probably we'll do a,b next time.
Homework 6; Due 11.30 a.m. FRIDAY November 13
Kelly: 4.1.10, 4.1.11, 4.2.1, 4.2.9, 4.3.3, 1.4.2
Hint for 4.3.3: the integrals get messy. You may use the result that
the integral from 0 to infinity of yke-y is
k!. (See Exx. 4.3.10, and the footnote at the bottom of P. 269.)
Homework 7; Due 11.30 a.m. MONDAY November 23
Kelly: 4.2.16, 1.Supp.11, 7.3.6, 7.3.7 (a)(b)(c), 6.4.4, 7.4.3.
1.Supp.11: Computers generate (to the limits of computer accuracy)
random numbers between 0 and 1, and would output them as a decimal. First digit here is first digit after the decimal point etc.
Homework 8; Due 11.30 a.m. Wed December 2
Kelly: 6.2.3, 6.2.5, 6.4.9, 6.4.13*, 6.4.14, 6.Supp.8
*: 6.4.13: Do both the exact answer and an appropriate approximation.
In all questions,
answers either with or without continuity correction are acceptable where
appropriate, but be REALLY clear exactly what you are doing.
Homework 9; Due 11.30 a.m. Wed December 9
Kelly: 1.4.4, 1.4.8, 2.2.16, 2.4.11, 3.3.9, 8.3.6 (b,c,e).
2.2.16, 2.4.11(b): be careful not to assume the answer; work from the
Poisson probabilities.
8.3.6 (b) Let Y be the numberof customers arriving in 10 minutes.
(c) X is sum of 100 independent exponentials; hence you know its
mean and variance.
(e) To get the book's answer, you will need to use a continuity
correction on this discrete Poisson r.v. Y.