A. Adhikari

PRACTICE PROBLEMS AND HOMEWORK

This page contains a weekly list of practice problems, including the subset that must be turned in to be graded as homework.

Recommended strategy:

Step 1. Go through your lecture notes carefully. This is important. Lecture is usually more succinct than the text and will always contain examples.

Alternative Step 1. Skim the text (see the Reading page). Note what the main ideas are and what techniques are being used in the examples. Read the text more carefully if you don't follow the examples.

Step 2. Try a problem.

Step 3. If you get stuck, return to Step 1.

Iterate a couple of times, reading more carefully each time and trying the same problem. Most likely you'll be able to solve it. If you still can't, only then:

Step 4. Move to another problem and seek help with the one that is giving trouble.

In my experience many students start with Step 2 and, if they get stuck, proceed immediately to Step 4. This method is inefficient and doesn't result in much learning. Before you come to me or to the GSIs or to the Student Learning Center, do the reading first! You may not need to make the trip at all.

Homework Requirements: Please make sure that your homework is easily identifiable as yours, easy to read, and doesn't come apart. In particular, your homework

- must be stapled (please don't use paper clips or other methods), and

- must have your name (legibly), SID number, and discussion section number (e.g. 101), and homework number (e.g HW 1; see the list below) on the top page.

Homework Grading: Papers will be graded on a 1/0 scale. Each assignment will consist of 8 problems. A good attempt at 6 or more problems will receive the score of 1; anything else will get 0. Course staff get to define "good attempt." We will be looking for reasoning and detailed work shown – it is assumed that you will show work or provide reasoning whether or not the question asks for it. Please do not copy other people's solutions; that includes answers found on the internet. Even if you feel you understand someone else's correct answer, copying creates an illusion of being able to do related problems without help; this might be cruelly shattered by exams.

Notation: In what follows, Exercise x.y.n is Problem n in the Exercises at the end of Section x.y. Exercise x.rev.n is Problem n in the Review Exercises at the end of Chapter x.

PLEASE DO NOT TURN HOMEWORK IN EARLY. IT WILL GET LOST.

WEEK 1.

Minimal practice: 1.1.7 (Example 2 will help), 1.3.3, 1.3.5,
1.3.7, 1.4.3, 1.4.5, 1.5.1, 1.5.5, 1.6.1, 1.6.5, 1.6.7a, 1. rev.7 (part d is on the next page)

Highly recommended: 1.3.6, 1.3.10, 1.3.11, 1.3.13, 1.5.6, 1.6.8, 1.rev.8, 1.rev.11, 1.rev.12, 1.rev.14, 1.rev.15, 1.rev.19

Homework 1 (due Wednesday 1/25):
1.1.8, 1.3.12, 1.4.6, 1.4.10, 1.5.2, 1.5.4, 1.6.6, 1.rev.16Highly recommended: 1.3.6, 1.3.10, 1.3.11, 1.3.13, 1.5.6, 1.6.8, 1.rev.8, 1.rev.11, 1.rev.12, 1.rev.14, 1.rev.15, 1.rev.19

WEEK 2.

Minimal practice: 2.1.1, 2.1.3, 2.1.5, 2.2.1, 2.2.5, 2.2.9

Highly recommended: 2.1.2, 2.1.7, 2.1.9, 2.1.10, 2.1.11, 2.2.2, 2.2.3, 2.2.4, 2.2.8, 2.2.12, 2.rev.8

Homework 2 (due Wednesday 2/1): 2.1.4, 2.1.6, 2.1.8, 2.1.12, 2.2.6, 2.2.10, 2.2.14, 2.rev.24 (be careful in part b)

WEEK 3.

Minimal practice: 2.4.3, 2.4.5, 2.4.7, 2.5.1, 2.5.7, 2.rev.15

Highly recommended: 2.4.2, 2.4.9, 2.5.2, 2.5.3, 2.5.4, 2.5.5, 2.5.9, 2.5.12 (the parts that aren't assigned for homework), 2.5.13, 2.rev.12, 2.rev.14, 2.rev.16, 2.rev.22, 2.rev.28

Homework 3 (due Wednesday 2/8): 2.4.1a,d (just those two parts; show some of your calculations and give the area of each bar that you draw; use a ruler!), 2.4.6, 2.4.8, 2.5.6, 2.5.8, 2.5.12a-e (just those five parts), 2.rev.10, 2.rev.18

WEEK 4.

Minimal practice: 3.1.3, 3.1.9, 3.1.15 (connect this with Example 3 of Section 1.1 and Exercise 1.1.8), 3.2.1, 3.2.3, 3.2.5, 3.2.7, 3.2.11

Highly recommended: 3.1.2, 3.1.6, 3.1.7, 3.1.10, 3.1.13, 3.2.6, 3.2.9, 3.2.13, 3.2.17, 3.2.16, 3.2.19

Homework 4 (due Wednesday 2/15): 3.1.8, 3.1.12, 3.1.14, 3.2.4, 3.2.14, 3.2.20, 3.rev.8, 3.rev.10

WEEK 5.

Minimal practice: 3.3.1, 3.3.3, 3.3.13, 3.3.19, 3.6.1, 3.6.7, 3.6.8

Highly recommended: 3.3.5, 3.3.7, 3.3.9, 3.3.15, 3.3.23, 3.6.9

Homework 5 (due Wednesday 2/22): 3.3.6, 3.3.8, 3.3.12, 3.3.16, 3.3.20, 3.6.2 (turn the page for part d), 3.6.5 (yes, it's an odd-numbered problem), 3.6.6

WEEK 6.

Minimal practice: 3.4.1, 3.4.3, 3.4.5, 3.5.1, 3.5.5, 3.5.11, 3.rev.15

Highly recommended: 3.4.2, 3.4.11, 3.5.2, 3.5.7, 3.5.9, 3.5.16, 3.rev.26

Homework 6 (due Wednesday 3/1): 3.4.10, 3.4.12, 3.4.14, 3.5.4 (say what you are assuming about the randomness), 3.5.10, 3.5.12, 3.5.17 (yes, it's an odd-numbered problem, and yes, the decimal answer is in the back of the book), 3.rev.2

WEEK 7.

Midterm week. No homework will be assigned this week, so no homework will be due on Wed 3/8.

WEEK 8.

Minimal practice: 4.1.1, 4.1.3 (parts d and e are on the next page), 4.1.9, 4.2.1, 4.2.5, 4.rev.3, 4.rev.13

Highly recommended: 4.1.2, 4.1.5, 4.1.10, 4.1.11, 4.2.6, 4.rev.4, 4.rev.12

Homework 8 (due Wednesday 3/15): 4.1.4, 4.1.7 (yes, it's an odd-numbered problem), 4.1.8, 4.1.12, 4.2.4, 4.2.8, 4.rev.2, 4.rev.14 (part c is on the next page)

Note: Careful about the variance calculation in 4.2.8. Many students calculate the expectation by weighted averaging, but that doesn't work for variances. If you can do part (a), then you should be able to find the density via the c.d.f. Use that to justify your expectation calculation, and then use the same method to find the expectation of the square of X. After that the variance is easy.

WEEK 9.

Minimal practice: 4.4.1, 4.4.3, 4.4.7, 4.5.3, 4.5.5, 4.6.1, 4.rev.5, 4.rev.18, 4.rev.21

Highly recommended: 4.4.5, 4.4.10, 4.5.4, 4.5.7, 4.rev.6, 4.rev.22, 4.rev.23

Homework 9 (due Wednesday 3/22): 4.4.2, 4.4.4, 4.4.6, 4.5.2, 4.5.6, 4.5.8, 4.rev.4 (please provide a sketch of the density), 4.rev.22

WEEK 10.

Minimal practice: 4.6.1, 4.6.5a, 4.rev.5, 4.rev.11 (do not crank them out by calculus; use what you know gamma and beta densities), 5.1.1, 5.1.7, 5.2.1, 5.2.3, 5.2.5, 5.2.11

Highly recommended: 4.6.3abcd, 4.6.5a-b, 5.1.2, 5.1.3, 5.2.4, 5.2.9, 5.2.10, 5.2.13, 5.rev.2

Homework 10 (due Wednesday 4/5): 4.6.2, 4.rev.16, 5.1.4, 5.1.6, 5.1.9 (let the stick have length 1; try drawing the right region), 5.2.6, 5.2.8, 5.2.12, 5.2.14, 5.2.16

SPRING BREAK

WEEK 11.

Minimal practice: 5.3.1, 5.3.3, 5.3.7 (turn page for more parts), 5.3.9, 5.3.11, 5.4.1, 5.4.3, 5.4.5, 5.rev.5

Highly recommended: 5.3.6 (it is helpful to draw figures as in 5.3.1), 5.4.4, 5.rev.2, 5.rev.16

Homework 11 (due Wednesday 4/12): 5.3.4, 5.3.8, 5.3.12, 5.4.10 (the easiest way is to use the c.d.f.), 5.4.13. 5.rev.12, 5.rev.22, 5.rev.24 (assume d < s; note that parts b and c are on the next page)

WEEK 12.

Minimal practice: 6.1.1, 6.1.3, 6.2.1, 6.2.3, 6.2.11, 6.3.1, 6.3.5

Highly recommended: 6.1.5, 6.1.7, 6.1.8, 6.2.7, 6.2.18 (done in class), 6.3.3, 6.3.7

Homework 12 (due Wednesday 4/19): 6.1.2, 6.1.8, 6.2.4 (for part (b), I recommend looking at page 487 where you will find the variance of a useful uniform variable), 6.2.10, 6.2.12, 6.2.16, 6.3.2, 6.3.4

WEEK 13.

Minimal practice: 6.4.3, 6.4.5, 6.4.9, 6.4.11, 6.4.19, 6.4.21

Highly recommended: 6.4.7, 6.4.11, 6.4.13, 6.4.15a-c (don't redo (a) to prove (b) - use (a) to prove (b)!),

Homework 13 (due Wednesday 4/26): 6.3.8, 6.3.10, 6.3.12, 6.4.8, 6.4.10, 6.4.12, 6.4.22, 6.rev.21

WEEK 14.

I can't assign homework this week as it would have to be due during RRR week. But you do need to learn the material of Section 6.5. Please work through the following problems from Exercises 6.5: 1, 2, 3, 4, 5, 6, 8, 12.