course information

Mathematics 20                Spring 2003           Syllabus

Date             Topics                                                                                 Homework

 3-26 1.2  Discrete probability distributions Hand in page 35:  2, 3, 4, 6, 22.  Do (don't hand in): 1, 5. 3-28 1.2 continued, 3.1 Counting Hand in page 35: 9, 11ac, 13, 18b.    Do(don't hand in): 25, 31a Hand in page 88: 2, 12                Do(don't hand in): 1, 3, 5

 3-31 3.1, 3.2  Counting, permutations, combinations Hand in page 88: 7; page 113: 1a,c,d,f,g, 2.  Also hand in:  A  permutation of the set {1, 2, 3} is chosen at random.  What is the probability that it does not have a fixed point?   Do on page 88: 17 and on page 113: 13. 4-2 More combinations, Pascal's triangle Hand in 3.1: 14;  3.2: 9, 20, 22.     Do 3.1: 13;  3.2: 19 4-4 Bernoulli trials Hand in 3.2: 1b,e, 6, 8, 10        Do 3.2: 7, 15.  In problem 10, use the program BinomialProbabilities available in Chapter 3 here.  (If necessary, read the instructions at the bottom of the page the link takes you to.)

 4-7 Inclusion-exclusion principle Hand in 3.2: 18, 34(a) and these two problems.   Some solutions 4-9 Conditional probablities Hand in 4.1: 1, 2, 5(a), 8, 24.       Do 4.1: 3, 7, 9, 29 4-11 Tree diagrams Hand in 4.1:  12, 16, 17(a), 19, 22.   Do: 13, 15, 23 (Just find a way to distrubute the balls so that P(a white ball) is > 1/2.)

 4-14 Independent random variables, expected value Hand in 4.1: 35, 39, and 6.1: 2, 4, 8.  Do 6.1: 3, 5 4-16 More expected values Hand in p. 36: 14, and 6.1: 14, 16(for part (b), just compute P(total = 21), 18, 20ab, 36.    Do 6.1: 17 4-18 Variance Hand in 6.1: 22(You'll need to use the BinomialProbabilities program for this) and 6.2: 2, 4, 12, 14.    Do 6.2: 3

The test on Monday, April 21 in Bradley 102 (our class room) from  7:00 to 9:00 covers up to and including material from class on  4-16.  You are not allowed to use a calculator during the test.   If you find you need one, you've probably made a mistake.  The test will be closed book and no formulas will be given, unless you convince me that some formulas are hard to remember, even if you  understand the content of the course well.

 4-21 More variance Hand in 6.2: 8, 10, 20                   Do: 7, 11, 15 4-23 Hand in 6.2: 27 and 5.1: 6, 7, 8 and problem 3 here.   Do 5.1: 1 4-25 Poisson distribution Hand in 5.1: 12, 14(a), 16,  22, 18, 20.     Do 5.1:  13, 17, 21, 25, 27.  Use the Poisson distribution on all of these, even if the instuctions don't explicitly say to approximate probablitities.

 4-28 More Poisson, start convolutions Hand in 5.1: 14(b);  6.1: 21; and problem 4 here;   Do 5.1: 23 4-30 Convolusions, Chebyshev's inequality Hand in 5.1: 32;  7.1: 2, 4(Just say what the probability is that you win 20 after 10 independent plays, and say which, among all possible winnings, is the most probable.   How is this related to your expected winnings?); 8.1: 1, 5.    Do: 7.1: 3 5-2 Law of Averages Hand in 8.1: 6, 8 and problem 5 here.     Do 8.1: 7, 9, 11

 5-5 Central limit theorem Hand in 9.1: 1ab, 2ab, 3                 Do 9.1: 1cd, 2c, 5, 9 5-7 More central limit theorem Hand in 9.1: 4(just for 499,000 and 501,000), 8, 12;  9.2: 2, 6; and problem 6 here.  Do  9.1: 13 and 9.2: 1, 5, 7 5-9 CLT and statistics Hand in 9.1: 14, 16   Do: 17, 18

The test on Monday, May 12 in Bradley 102 (our class room) from  7:00 to 9:00 will cover material from classes on  4-18 through 5-7.  You are not allowed to use a calculator during the test.   If you find you need one, you've probably made a mistake.  The test will be closed book and no formulas will be given.

 5-12 test 5-14 Start Markov chains Hand in 11.1: 2, 4, 6(w should be u, as in Theorem 11.2 on page 407), 8, 12     Do 11.1: 3, 5, 7, 11 5-16 Absorbing chains Hand in 11.2: 2, 4, 18ab and problem 7 here.    Do: 1, 3, 5(first part)

 5-19 More absorbing chains Hand in 11.2: 6, 8, 9     Do 11.2: 5, 15, 18c(answer is .67) 5-21 Regular Markov chains Hand in 11.3:  2ab, 10(11.10 in on p. 411)  and Problem 8 here.  Do 11.3: 1, 3, 11 5-23 Ergodic Markov chains Hand in 11.3:  2c, 4, 24  and 11.5: 2b, 6  (Due Wed., the 28th, but if it's in the box by noon Monday, the 26th, it will be graded by Wed.)  Do 11.3:  5, 13 and  11.5:  3, 7

 5-28 Mean recurrence times Suggested  11.5:  2a(answer: 4.5), 4(answer:1+a/b for yes, 1+b/a for no), 5

Final exam:  Saturday, 5/31, 8:00-10:00, Bradley 102.
The final exam will cover the entire course, but will emphasize material covered since the second exam.