Homework and Test Schedule

Math 20 Summer term 2000

This page will be changed on an almost daily basis, so check back frequently. In particular the homework due on a given day may be changed any time up until noon on the previous class day.

In the reading, i.j stands for Section j of Chapter i of the book by Grinstead and Snell

Date Due	Topics	Reading	Problems Assigned
6/25	Basic Probability	1.2	p35. #1, 2, 3(see p 25 for "uniform distribution"), 4, 5, 6,14
6/27	Basic Probability	1.2	p35. #9, 11ac, 13, 18, 21, 25, 31
6/29	Combinatorics	3.1	p88. 1, 2, 3, 7, 10, 14, 17
7/2	"Combinations"	3.2	p112. 1a,c,d,f,g, 2, 9, 12a-d, 13 (Hint: when is C(n,k) smaller than C(n,k+1) [using C(n,k) for "n choose k"]?), 22, 23
7/6	More Combinations	3.2	p112. 1b, e, h, 7, 8, 10, 31 (To do this problem, you do need to make a very modest assumption; if this hint confuses you, just ignore it, or blitz me with a question.)
7/9	Still more Combinations	3.2	p112. 6, 15, 18, You take a joke gift to a holiday party, as does everyone invited. The host mixes up all the gifts and passes them out at random to the guests. Assuming there are ten guests, what is the probability you get the gift you took? What is the probability that some person gets the gift he or she took?, 34, A seminar room has n chairs. There are k students in the room for a seminar. The seminar takes a tea break, and every student leaves the room. Assuming they choose seats randomly when they return, what is the probability that no student is sitting in the seat in which he or she sat previously?
7/11	Conditional Probability	4.1	P150. 1, 2, 3, 5a, 7, 8, 9 Hint: use tree diagrams., 14
7/13	More Conditional Probability	4.1	P 150. 12, 13, 15, 17a, 23, 35, 39
7/16	Conditional Probability and Expected Values	4.1, 6.1	P 150. 22,24; P247. 2,3,4,8
7/17	Class in X-hour		No homework due
7/18	Exam 7PM		Bring Questions to class for Q and A session, no homework due
7/20	No Class	6.1	Homework Due in Homework boxes at 11:15 Friday 7/20 P247 #5, 15, 19, 22 (You will need a calculator or computer here.), 36, A nickel, two dimes and two quarters are in a cup and a child draws two coins, one after another. What is the expected amount of money drawn on the first draw? On the second draw? Explain any similarity or difference in your answers. What is the expected total amount of money drawn?
7/23	More Expected Values	6.1	P247 #13, 14, 18, 20, 35
7/25	Variance	6.2	P263 #1, 2, 4, 5, 7, 12, 14
7/27	More Variance	6.2	P263 #10, 15, 18, 20, 21, 27
7/30	Important Distributions	5.1	P197 #1, 4, 6, 7, 8, Let X be the random variable that counts the number of times we have to roll a die until we have seen all six numbers on top. Find the expected value of X. Hint: Try the problem first with X equal to the number of times we have to roll a die until we have seen two different numbers on top, then three different numbers on top.
8/1	Important Distributions	5.1	P197 #12, 13, 22, p250 #21 p268 #30 Hints: What is the power series for x times e to the x? What is the derivative of that power series?
8/3	Important Distributions	5.1	P197 #11,14,18, 23, 28, 32 Hint: Once you get going with the algebra and can't see what to do next, look for an application of the binomial theorem.
8/6	Law of Large Numbers	8.1	P312 #1, 5, 6, 7, 8, 9
8/8	Exam #2		7PM Room 012 Bradley
8/10	Central Limit Theorem	9.1	P338 #1, 2, 4, 7, 12 Guest Lecture Friday: Prof. Snell
8/13	Card Shuffling	3.3	1. If you have a deck of n cards, the ìtop inî shuffle is a shuffle in which you take the top card and move it randomly behind one of the cards. Thus if we start with (1,2,3), then we have a 1/3 chance of changing it to each of (1,2,3), (2,1,3) and (2,3,1). Find the probability for each possible arrangement after two top-in shuffles using this three-card deck. Find the variation distance. 2. Assume that you have a three-card deck and do two riffle shuffles starting with the arrangement (1,2,3). Find the probability for each arrangement and the variation distance. Which of the two methods, top-in or riffle shuffles, gives the best (in the sense of variation distance) result for two shuffles of a three-card deck?
8/15	Central Limit Theorem	9.1,9.2	P338 #16,17,18. p352 #1,3, 5
8/17	Markov Chains	11.1	P413 #3, 4, 5, 11, 12, 18 (You will have to read about the vector u.)
8/20	Absorbing Chains	11.2	P422 #2, 3, 5, 8, 15, 34
8/25	Final Exam		The exam is scheduled from 9 to 11 AM in room 102 Bradley. I will be there with the exams at 8AM for anyone who would like 3 hours.
8/22	Regular Chains	11.3	P422 #1, 2, 5a, 16, 24, 26. There will be a question and answer session in class on 8/22. So we can be more efficient, please blitz Prof. Bogart with questions in advance if you can. (Remember he has a 10 class also!)