Stat 433: Homework

Homework 1 (solutions)

• Read: pp 1-15, 57 - 68, 87 - 93.
• I.2 Exercises (p 19): 1, 3, 5, 10
• I.2 Problems (p 21): 12
• II.1 Exercises (p 61): 2, 6
• II.1 Problems (p 62): 6, 10
• (if you don't have the book yet here is the chapter: .pdf)

Homework 2 (solutions)

• Reread 87 - 93. Read: p 95 - 104
• II.5 Exercises (p 93): 2, 3
• II.5 Problems (p 94): 1, 2, 4
• III.1 Problems (p 99): 1
• (if you don't have the book yet here is the chapter: .pdf)

Homework 3 (solutions)

• Read Chapter 3 up to page 112
• III.1 Exercises (p 98): 3
• III.1 Problems (p 100): 4
• III.2 Exercises (p 102): 2
• III.2 Problems (p 104): 1, 2
• III.3 exercises (p 112): 1

Homework 4 (solutions)

• Read carefully p 116 - 130 (Then read it again!) This will probably take about 3 hours.
• II.5 Problems (p 94): 5
• III.4 Exercises (p 127): 1, 3, 4, 5
• III.4 Problems (p 130): 1, 7, 17

Homework 5 ( answers)

• Read 136 - 147.
• III.4 Exercises (p 127): 7, 9
• III.4 Problems (p 130): 4, 6, 10
• III.5 Exercises (p 148): 2, 7
• III.5 Problems (p 150): 3, 5 (note the maximal inequality this problem mentions is on page 90.)

Homework 6 solutions

• p 183 # 8.1, 8.3
• p 184 # 8.2, 8.4
• Read p 199 - 208
• IV.1: exercises (p 208): 1.1, 1.4

• Here are two midterms from previous years:
  • 2004 (answers)
  • Another midterm (no answers)
• p 63 # 1.7 (exam level of difficulty)
• The following are about random sums. Treat the last 3 as homework level difficult problems.
  • p 77 # 3.1 (exam level of difficulty)
  • p 78 # 3.3 (exam level of difficulty)
  • p 78 problem 3.1, 3.3, 3.4
• p 94. # 5.3 (look over the other martingale problems in this section. Be sure you think they are easy now! If not--try them again.)
• p 99 exercise 1.5: (exam level of difficulty)
• p 99 problem 1.1: (exam level of difficulty)
• p 103 # 2.5
• p 104 # 2.3
• p 112 # 3.2
• p 114 # 3.4
• p 127 # 4.2 (exam level of difficulty)
• p 129 # 4.8 (exam level of difficulty)
• p 130 # 4.2
• p 132 # 4.8 (exam level of difficulty)
• p 148 # 5.8
• p 150 # 5.1

Homework 7 (solutions)

• Read p 216 - 230
• IV.1: exercise (p 210): 1.8
• IV.1: problems (p 211): 1.1, 1.2, 1.6, 1.10, 1.12
• IV.2: exercises (p 229): 2.5, 2.8
• Consider a sequence of coin tosses, using the method discussed in Mike Steele's lecture:
  • On average how long will it take to get the pattern H,H,T,H?
  • On average how long will it take to get the pattern T,H,H,H?

Homework 8 (solutions)

• Read p 234 - 244
• IV.2: problems (p 230): 2.2, 2.6, 2.7
• IV.3: exercises (p 243): 3.1, 3.3
• IV.3: problems (p 245): 3.1

Homework 9 (solutions)

• Read p 267 - 286
• V.1: exercises (p 274): 1.3, 1.7, 1.9
• V.1: Problems (p 275): 1.1, 1.7
• V.2: exercises (p 286): 2.4

Homework 10 ( solutions)

• Read carefully 290-294 to see the "analysis" version of the proof I covered in class.
• Read 297-305
• V.2: problems (p 287): 2.2, 2.4, 2.10, 2.11
• V.3: exercises (p 294): 3.8
• V.3: problems (p 295): 3.3, 3.8
• V.4: exercises (p 308): 4.3
• V.4: problems (p 309): 4.6, 4.8

Homework 11 ( solutions)

• V.4: problems (p 309): 4.9
• V.5 exercises (315): 5.1
• V.5 problems (316): 5.4, 5.5
• V.6 exercises (328):6.2
• V.6 problems (329):6.3, 6.10
• read p 333 - 340 (all of section 6.1)
• VI.1: exercises (p 341): 1.2, 1.3
• read p 345 - 349 (first part of section 6.2)
• VI.2: exercises (p 353): 2.1, 2.4

Homework 12 ( solutions)

• read p 355 - 364 (all of section 6.3)
• VI.1: problems (p 342): 1.2, 1.3, 1.6
• VI.2: problems (p 354): 2.1, 2.3, 2.4
• VI.3: exercises (p 364): 3.2
• VI.3: problems (p 365): 3.2

Homework 13 ( solutions)

• Optional: Read section 6.6 if you have taken linear algerbra.
• Read section 8.1: up to page 481.
• Read all of 8.2

Sample final. (answers). Note, E(Y|Y) = Y, not E(Y|Y)=1 as the answer key suggests.

Another sample without answers final. (and the answers) Note: the "double cross" problem is really too hard for an exam question, so ignore it!

You will be allowed one new cheat sheet along with the one you made for the midterm. (no calculators on the exam)

Some questions that might be useful for review.

• page 210: 1.8, 1.10
• page 211: 1.3
• page 243: 3.2
• page 256: 4.2
• page 258: 4.7
• page 274: 1.4, 1.6
• page 276: 1.3, 1.7
• page 287: 2.4
• page 288: 2.4
• page 294: 3.3, 3.5
• page 309: (exercise) 4.5, (problem) 4.2
• page 341: 1.3, 1.5
• page 364: 3.1, (and 3.2 which should look familiar!)

• page 487: 1.4, 1.5 (but not covered on the exam)
• page 488: 1.6 (also not covered on the exam)