Mathematics 20
Spring 2003
Syllabus
| 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 |
| 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 |
| 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 |