Homework Math115-001: DONAGI

Assignment #1: Due Thursday, January 15, at 4pm. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Read all material on the course web page.

Print out and sign the STUDENT'S PERSONAL STATEMENT at the end of the class rules.

Do the core problems from section 12.1: # 5,8,13,14,15,16,17,18,19,25,45.

Assignment #2: Due Thursday, January 22, at 4pm. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Do the core problems from section 12.2: # 11,13,16,35.

Do the core problems from section 12.3: # 5,19,30,47,57,63,65.

Assignment #3: Due Thursday, January 29, at 4pm. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Do the core problems from section 12.4: # 5,11,20,23,24,34a.

Do the core problems from section 12.5: # 3,8,17,40,41.

Do the core problems from section 12.7: # 2,3,17,18.

Do the core problems from section 12.8: # 6,11,17,29,36,39,42,53.

Assignment #4: Due Thursday, February 5, at 4pm. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Core problems.

Do the (postponed) core problems from section 12.7: # 27,31,43,55.
Do the core problems from section 12.9: # 5,14,21,23,32,46.
Do the core problems from section 13.1: # 5,8,15,21,23,26,29,33,45,53,54.

Mock tests. The material for these mock tests is taken from the "Sample final exams" and "Old final exams" sections of the course web site. (The sample exams, but not the old exam, can also be found in the lab manual.) Please time yourself: you should be able to complete each test in 35 minutes, including some time for checking your answers. In other words, you have a little less than 6 minutes per problem! It is crucial that you work fast. If it takes you longer than 6 minutes per problem, you must practice working faster. Use the first test to help you identify topics with which you need more practice or some help. Make sure you work on these topics before attempting the second test.

Mock test #1: "Sample Final Exam #1" , problems 8-13. (6 problems, 35 minutes.)
Mock test #2: "Old final exam 2002" , problems 1-6. (6 problems, 35 minutes.)

Assignment #5: Due Friday, February 13, at noon.

More mock tests. The material for these mock tests is taken from the "Sample final exams" section of the course web site. (They can also be found in the lab manual.) Just as you did last week, please time yourself: you should be able to complete each test in 35 minutes, including some time for checking your answers. In other words, you have a little less than 6 minutes per problem. It is crucial that you work fast. If it takes you longer than 6 minutes per problem, you must practice working faster. Use the first test to help you identify topics with which you need more practice or some help. Make sure you work on these topics before attempting the second test. By the time you have completed the two tests from last week plus the two below, you should be in great shape for the midterm exam.

Mock test #3: "Sample Final Exam #2" , problems 9-14. (6 problems, 35 minutes.)
Mock test #4: "Sample Final Exam #3" , problems 9-13. (5 problems, 30 minutes.)

New material, from the Probability text:

Read Chapter 1, sections 1-7.
Do the core problems from section 1.5: #7,8.
Do the core problems from section 1.7: #1,3,4,5,7,8.

Assignment #6: Due Thursday, February 19, at 4pm. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Core problems, from the Probability text:

Do the core problems from section 1.6: # 1,2,3,4
Do the core problems from section 1.8: # 2,3,4,7,17,18
Do the core problems from section 1.9: # 1,3,6,8
Do the core problems from section 1.10: # 1,4,5,6,9

Assignment #7: Due Friday, February 27, at noon. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Core problems, from the Probability text:

Do the core problems from section 2.1: # 6,9,10.
Do the core problems from section 2.2: #7,8,9,10,12,16,19
Do the core problems from section 2.3: # 1,2,10,11,12
Do the core problems from section 3.1: # 2,3,4,8
Do the core problems from section 3.2: # 2,3,4,5,6,7,8

Extra credit problems. Many of you have asked for these, so here is a first batch. Optional, of course:

Vectors: Lab Manual, pages 320-322, #9-12.
Calulus with Maple: Lab Manual, page 323, #1
Curves: Lab Manual, pages 326-327, #17-20.

Assignment #8: Due Friday, March 5, at noon. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Core problems, from the Probability text:

Do the core problems from section 3.3: # 3,4,5,6,7,8.
Do the core problems from section 4.1: #1,2,4,5,9
Do the core problems from section 4.2: #6,7,8,10
Do the core problems from section 4.3: #1,2,3,6,7,9.

Extra credit problems, second batch. Optional, of course:

Taylor: Lab Manual, pages 328-329, #23.
Probability text, section 1.12 #13.
Find a recent (i.e. 2004) news article which uses bogus or misleading arguments from probability or statistics. Explain the error and give the correct version.

Assignment #9: Due Friday, March 19, at noon. (You may instead hand in your homework assignment on Thursday, AFTER CLASS.)

Core problems, from Chapter 5 of the Probability text:

Do the core problems from section 5.2: # 3-7,10
Do the core problems from section 5.4: #2,3,6
Do the core problems from section 5.6: #3,7,9,10
Do the core problems from section 5.9: #8,9,13,14

Assignment #10: Due Friday, March 26, at noon.

Mock tests. The material for these mock tests is taken from the "Sample final exams" section of the course web site. (Most can also be found in the lab manual.) Each of these five tests is about one half the length of the midterm. The exact time allowed for each test is stated below. Please time yourself: you should be able to complete each test in the alotted time, but be sure to leave some time for checking your answers. In other words, you have a little less than 6 minutes per problem. It is crucial that you work fast. If it takes you longer than 6 minutes per problem, you must practice working faster. Use the first test to help you identify topics with which you need more practice or some help. Make sure you work on these topics before attempting the second test, and so on.

In addition to these five tests, Corey and I will hand out copies of Professor Powers' second midterm. (You can get them from Corey in recitation, from me in class, or from either of us in office hours.) This is not part of the homework assignment (so you do not need to hand it in), but we will go over it in class as part of our preparation for teh midterm. His test does not cover all of our material (e.g. continuous distributions are missing). Problems 1-12 of his test are relevant to us.

In class on Thursday we will discuss Professor Powers' second midterm, as well as Mock tests #1 and #5, as time permits. So in order to derive the most benefit from this procedure, please be sure to completely solve these two mock tests before Thursday, and at least have a look at Powers' test to make sure you know which technique applies to each problem. This way, by the time you have completed the six tests, you should be in GREAT shape for the midterm exam.

Mock test #1: "Sample Final Exam #1" , problems 1-7. (7 problems, 42 minutes.)
Mock test #2: "Sample Final Exam #2" , problems 1-8. (8 problems, 48 minutes.)
Mock test #3: "Sample Final Exam #3" , problems 1-8. (8 problems, 48 minutes.)
Mock test #4: "Sample Final Exam #4" , problems 1-8. (8 problems, 48 minutes.)
Mock test #5: "Old final exam 2002" , problems 7-14. (8 problems, 48 minutes.)

Assignment #11: Due Friday, April 2, at noon.

Problems from the Probability text:

Do the problems from section 3.4: # 1,2,4,6.
Do the problems from section 3.5 # 1,3,4,6,7,8,11
Do the problems from section 1.10 # 8,9,10,11.

More problems on bivariate distributions:

1. Suppose the joint p.d.f. of a pair of random variables on the rectangle 0 < x < 2, 0 < y < 1 is given by f(x,y) = 1/2. Compute Prob(X > Y).

2. Suppose the joint p.d.f. of a pair of random variables on the rectangle 0 < x < 2, 0 < y < 1 is given by f(x,y) = xy. Compute Prob(X > Y)

3. Suppose the joint p.d.f. of a pair of random variables on the first quadrant 0 < x, 0 < y is given by f(x,y) = 6exp(-(2x+3y)) (exp(x) = e^x). Assume a > 0.
Compute Prob(X > a), Prob(Y > a), Prob(min(X,Y) > a), Prob(X > Y)

4. Suppose the joint p.d.f of n-random variables x(k), k = 1,...,n on the region 0 < x(k) < 2 for k = 1,...,n is f(x) = 1/(2^n). Let Y = x(1) + x(2) + .... + x(n)
Compute E(Y) and E(Y^2).
Hint. For independent random variables we have the means and variances add.

Assignment #12: Due Friday, April 9, at noon.

Problems from the Linear Algebra text:

Do the problems from section 1.3: # 8,10,11,17
Do the problems from section 2.1: # 23,25,29
Do the problems from section 2.2: # 17,24,27,28,33,39,40
Do the problems from section 2.3: # 27,29

Assignment #13: Due Friday, April 16, at noon.

Problems from the Linear Algebra text:

Do the problems from section 2.4: # 15,24,30,31
Do the problems from section 2.5: # 11,13,15,17,19,22,23
Do the problems from section 2.6: # 1,5,17

Problems from the Probability text:

Do the problems from section 2.4: # 2,3,11,12 (also find the limiting distribution for each).

Assignment #14: Due Friday, April 23, at noon.

Do the following exam problems, mostly on linear algebra:

"Sample Final Exam #1" , problems 14,15,18.
"Sample Final Exam #2" , problems 15-19.
"Sample Final Exam #3" , problems 14-16.
"Sample Final Exam #4" , problems 9-16. (These include some calc problems.)
"Old final exam 2002" , problems 15-17 and (probability problem) #19.

Review all core, old exam, and final exam problems. Do not hand them in again - but be sure to write down any questions you have, and bring them to the various review sessions and office hours.

I know it's been a lot of hard work. I hope you feel that the knowledge you gained was worth the effort though. And maybe you've even had some fun along the way - as did I.

Good luck on the final, and have an exciting and rejuvenating summer,

Ron