Math 475-001 (Ellis) Fall 2007 IIT Applied Mathematics

MATH 475-001 Probability (Ellis) Fall 2007

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Instructor: Robert Ellis	Office: E1 Bldg, Rm 105C	Email:
Lectures	MWF 3:15-4:30pm	PH 108
	IIT 475 Section Schedule
Office Hours	M 2:00-3:00pm (Math 152 Priority) T 11:20am-12:20pm (General) W 1:15-2:15pm (Math 475 Priority) F 8:30-9:30am (General)	Office phone 567-5336
	Appointments and emailed questions are welcome
Textbook	Wackerly, Mendenhall, Scheaffer, Mathematical Statistics with Applications, 6th edition, Duxbury.

First day handout (course contract & exam schedule)

Exam and Solutions

Exam 1 Exam 2 Exam 3

1A (exam, key)
1B (exam, key)
Formula page 2A (exam, key)
2B (exam, key) 3A (exam, key)
3B (exam, key)

Homework Due Dates
Recommended exercises are a combination of practice for material on exams and advanced problems to test your knowledge.

W 9/5, 3:15pm Sect. 2.3, p24: 2.4, 2.6
Sect. 2.4, p31: 2.8, 2.14
Sect. 2.5, p37: 2.22, 2.26
The following problem must be done but is not to turn in: Follow the instructions to set up Virtual Laboratories in Probability and Statistics¹
Under the Section Foundations, run the "Venn Diagram Applet". Sketch the Venn Diagram for each set expression and then click to verify each answer.
Sect. 2.1-2.9 Sect. 2.3, p24: 2.1, 2.5
Sect. 2.4, p31: 2.9, 2.11, 2.13, 2.17
Sect. 2.5, p37: 2.19, 2.21, 2.23, 2.25

F 9/14, 5pm, in mailbox E1 Rm210 Sect. 2.6, p49: 2.30, 2.34, 2.35
Remember: No credit for answers without explanation.

F 9/14, 5pm, in mailbox E1 Rm210 Sect. 2.6, p49: 2.52
Sect. 2.7, p53: 2.58, 2.60, 2.62 (assume P(A)>0,P(B)>0), 2.64
Sect. 2.8, p57: 2.68, 2.70
Problem A: The following problem must be done with collected data turned in:
Read the short section "The Law of Large Numbers" here. Read the exposition on "Conditional Probability" here, paying special attention to question 3 on correlation. For now you may ignore other topics such as Bayes' Rule. Run the dice experiment in problem 13, except repeat 50 times instead of 500. Follow the rest of the directions of problem 13 to write down the empirical conditional probabilities as described. Sect. 2.1-2.9 Sect. 2.6, p49: 2.41, 2.43, 2.47, 2.53, 2.55
Sect. 2.7, p43: 2.57, 2.59, 2.61, 2.63, 2.65
Sect. 2.8, p57: 2.69, 2.71

F 9/21, 5pm, in mailbox E1 Rm210 Sect. 2.8, p57: 2.74, 2.80, 2.82 (assume 2.80 is true and express your answer as an inequality)
Sect. 2.9, p65: 2.88, 2.94, 2.96
Sect. 2.10, p69: 2.100, 2.108, 2.114
And: Work Problem 4ab at this page on independence. Run the experiment in Problem 5 if you need to build intuition. Sect. 2.10-2.13 Sect. 2.8, p57: 2.79, 2.80, 2.81, 2.83, 2.85
Sect. 2.9, p65: 2.87, 2.89, 2.91 (4-wise independence), 2.95, 2.97
Sect. 2.10, p69: 2.99, 2.101, 2.107, 2.113, 2.115, 2.116 (challenge)

F 10/5 5pm, E1 Rm210
1st of 2 parts Sect. 3.2, p87: 3.2, 3.6
Sect. 3.3, p95: 3.10, 3.12 (you may quote answer to 2.97)
Problem A. Play UCSD's Monty Hall game, and read the explanation. Read also a comparable Wikipedia explanation (Problem A has no hand-in component). Sect. 3.1-3.3 Sect. 3.2, p87: 3.3, 3.5, 3.7, 3.9
Sect. 3.3, p95: 3.11, 3.13, 3.19, 3.23

F 10/5 5pm, E1 Rm210
2nd of 2 parts Sect. 3.3, p95: 3.18, 3.20
Sect. 3.4, p106: 3.34, 3.38, 3.42, 3.48 Sect. 3.4-3.8 Sect. 3.4, p106: 3.25, 3.29, 3.33, 3.41, 3.43; challenge: 3.47, 3.49

F 10/12 5pm, E1 Rm210
Sect. 3.5, p114: 3.56, 3.58, 3.62, 3.68
Sect. 3.6, p118: 3.76, 3.78
Sect. 3.7, p123: 3.84, 3.90, 3.96
Problem A: #21(ab) at UAH's "The Negative Binomial Distribution page. (Turn in your answers.)
Remember, you must show work to guarantee full credit. Sect. 3.7-3.10 Sect. 3.5, p114: 3.51, 3.53, 3.55, 3.55, 3.59, 3.65, 3.67; challenge: 3.69-3.71
Sect. 3.6, p118: 3.73, 3.75; challenge: 3.80, 3.82, 3.83
Sect. 3.7, p123: 3.85, 3.87, 3.91, 3.95

M 10/22 3:15pm, in class
Sect. 3.9, p135: 3.116, 3.120, 3.124
Problem A: #12, UAH's Generating Functions page
Sect. 3.11, p141: 3.134, 3.138, 3.140 Sect. 3.11, 3.12, 4.1-4.3 Sect. 3.9, p135: book back right inside cover, 3.115, 3.117, 3.119, 3.121, 3.123, 3.125; challenge: 3.126, 3.127
Sect. 3.11, p141: 3.131, 3.133, 3.137, 3.141, 3.143

F 10/26 5pm, E1 Rm210
Sect. 4.2, p159: 4.4, 4.8, 4.12
Sect. 4.3, p164: 4.16, 4.20a, 4.24, 4.26
Sect. 4.4, p168: 4.30, 4.42
Sect. 4.5, p173: 4.46, 4.62, 4.64 4.4-4.7 Sect. 4.2, p159: 4.1, 4.3, 4.7, 4.11, 4.13
Sect. 4.3, p164: 4.15, 4.17, 4.19, 4.25, 4.27
Sect. 4.4, p168: 4.29, 4.31, 4.43, 4.45
Sect. 4.5, p173: 4.47, 4.53, 4.55, 4.59, 4.63, 4.65

M 11/12 3:15pm
in class Sect. 4.6, p180: 4.72, 4.86
Sect. 4.7, p185: 4.92 4.100
Sect. 4.9, p193: 4.104, 4.108, 4.112
Sect. 4.10, p196: 4.118 (see p10)
Sect. 5.2, p218: 5.4, 5.6, 5.10 4.8-5.4 Sect. 4.6, p180: 4.67, 4.71, 4.75, 4.79, challenge: 4.89, 4.90
Sect. 4.7, p185: 4.91, 4.95, 4.97
Sect. 4.9, p193: 4.105, 4.106, 4.109, 4.113
Sect. 4.10, p196: 4.115, 4.117
Sect. 5.2, p218: 5.1, 5.3, 5.7, 5.9

F 11/16 5pm, E1 Rm210
Sect. 3.8, p129: 3.108 (assume Poisson distribution)
Sect. 5.3, p229: 5.20, 5.22, 5.32
Sect. 5.4, p238: 5.42, 5.44, 5.30, 5.54, 5.56
Sect. 5.6, p247: 5.64, 5.72, 5.70 (assume y_1>0)
5.5-5.11 Sect. 3.8, p129: 3.97, 3.101, 3.107, 3.111, 3.114
Sect. 5.3, p229: 5.17, 5.19, 5.21, 5.23; challenge: 5.33, 5.35
Sect. 5.4, p238: 5.37, 5.39, 5.43, 5.45, 5.49, 5.53, 5.55, 5.57, 5.59, 5.61
Sect. 5.6, p247: 5.63, 5.65, 5.69; challenge: 5.73, 5.74

M 11/26 3:15pm, PH 108
WARNING: Answers only, or very little justification = no credit. I am assigning odd problems so you can have more feedback before the exam on 11/28.
The solutions will be posted to these problems on 11/26; you can keep a photocopy of your homework to correct and study for the exam.
Sect. 5.7, p253: 5.77, 5.81, 5.83 (read bottom half of p.250)
Sect. 5.8, p261: 5.87, 5.91, 5.95 (use Tshebycheff)
Sect. 6.3, p291: 6.3, 6.9 (average life=(Y1+Y2)/2), 6.11
Sect. 6.4, p300: 6.21, 6.27 6.1-6.5 Sect. 5.7, p253: 5.75, 5.79, 5.85
Sect. 5.8, p261: 5.86, 5.88, 5.89, 5.93, challenge: 5.97
Sect. 6.3, p291: 6.1, 6.5, 6.7, 6.13, 6.15; challenge: 6.17-6.18
Sect. 6.4, p300: 6.19, 6.23, 6.31, 6.32

W 12/5 3:15pm, PH 108
Final Homework. Pick up in office hours, 1-2pm, T/W Dec 11/12
Sect. 6.5, p307: 6.36, 6.40, 6.44
Sect. 6.6, p300: 6.54, 6.56 (Hint: for 6.54 use definition of gamma function, p176)
Sect. 7.2, p342: 7.2(a-c), 7.4 6.6, 7.1-7.3
recommended but optional: 7.4-7.5 Sect. 6.5, p307: 6.35, 6.37, 6.41, 6.43, 6.45, 6.47, 6.49, 6.51
Sect. 6.6, p300: 6.53, 6.55, 6.57
Sect. 7.2, p342: 7.1, 7.3, 7.7, 7.11

Due Date Problems to hand in Reading Recommended exercises

[1] Copyright holder of "Virtual Laboratories in Probability and Statistics" is Prof. Kyle Siegrist, Department of Mathematical Sciences, University of Alabama at Huntsville.

Exam and Solutions
Exam 1	Exam 2	Exam 3
1A (exam, key) 1B (exam, key) Formula page	2A (exam, key) 2B (exam, key)	3A (exam, key) 3B (exam, key)

W 9/5, 3:15pm	Sect. 2.3, p24: 2.4, 2.6 Sect. 2.4, p31: 2.8, 2.14 Sect. 2.5, p37: 2.22, 2.26 The following problem must be done but is not to turn in: Follow the instructions to set up Virtual Laboratories in Probability and Statistics¹ Under the Section Foundations, run the "Venn Diagram Applet". Sketch the Venn Diagram for each set expression and then click to verify each answer.	Sect. 2.1-2.9	Sect. 2.3, p24: 2.1, 2.5 Sect. 2.4, p31: 2.9, 2.11, 2.13, 2.17 Sect. 2.5, p37: 2.19, 2.21, 2.23, 2.25
F 9/14, 5pm, in mailbox E1 Rm210	Sect. 2.6, p49: 2.30, 2.34, 2.35 Remember: No credit for answers without explanation.
F 9/14, 5pm, in mailbox E1 Rm210	Sect. 2.6, p49: 2.52 Sect. 2.7, p53: 2.58, 2.60, 2.62 (assume P(A)>0,P(B)>0), 2.64 Sect. 2.8, p57: 2.68, 2.70 Problem A: The following problem must be done with collected data turned in: Read the short section "The Law of Large Numbers" here. Read the exposition on "Conditional Probability" here, paying special attention to question 3 on correlation. For now you may ignore other topics such as Bayes' Rule. Run the dice experiment in problem 13, except repeat 50 times instead of 500. Follow the rest of the directions of problem 13 to write down the empirical conditional probabilities as described.	Sect. 2.1-2.9	Sect. 2.6, p49: 2.41, 2.43, 2.47, 2.53, 2.55 Sect. 2.7, p43: 2.57, 2.59, 2.61, 2.63, 2.65 Sect. 2.8, p57: 2.69, 2.71
F 9/21, 5pm, in mailbox E1 Rm210	Sect. 2.8, p57: 2.74, 2.80, 2.82 (assume 2.80 is true and express your answer as an inequality) Sect. 2.9, p65: 2.88, 2.94, 2.96 Sect. 2.10, p69: 2.100, 2.108, 2.114 And: Work Problem 4ab at this page on independence. Run the experiment in Problem 5 if you need to build intuition.	Sect. 2.10-2.13	Sect. 2.8, p57: 2.79, 2.80, 2.81, 2.83, 2.85 Sect. 2.9, p65: 2.87, 2.89, 2.91 (4-wise independence), 2.95, 2.97 Sect. 2.10, p69: 2.99, 2.101, 2.107, 2.113, 2.115, 2.116 (challenge)
F 10/5 5pm, E1 Rm210 1st of 2 parts	Sect. 3.2, p87: 3.2, 3.6 Sect. 3.3, p95: 3.10, 3.12 (you may quote answer to 2.97) Problem A. Play UCSD's Monty Hall game, and read the explanation. Read also a comparable Wikipedia explanation (Problem A has no hand-in component).	Sect. 3.1-3.3	Sect. 3.2, p87: 3.3, 3.5, 3.7, 3.9 Sect. 3.3, p95: 3.11, 3.13, 3.19, 3.23
F 10/5 5pm, E1 Rm210 2nd of 2 parts	Sect. 3.3, p95: 3.18, 3.20 Sect. 3.4, p106: 3.34, 3.38, 3.42, 3.48	Sect. 3.4-3.8	Sect. 3.4, p106: 3.25, 3.29, 3.33, 3.41, 3.43; challenge: 3.47, 3.49
F 10/12 5pm, E1 Rm210	Sect. 3.5, p114: 3.56, 3.58, 3.62, 3.68 Sect. 3.6, p118: 3.76, 3.78 Sect. 3.7, p123: 3.84, 3.90, 3.96 Problem A: #21(ab) at UAH's "The Negative Binomial Distribution page. (Turn in your answers.) Remember, you must show work to guarantee full credit.	Sect. 3.7-3.10	Sect. 3.5, p114: 3.51, 3.53, 3.55, 3.55, 3.59, 3.65, 3.67; challenge: 3.69-3.71 Sect. 3.6, p118: 3.73, 3.75; challenge: 3.80, 3.82, 3.83 Sect. 3.7, p123: 3.85, 3.87, 3.91, 3.95
M 10/22 3:15pm, in class	Sect. 3.9, p135: 3.116, 3.120, 3.124 Problem A: #12, UAH's Generating Functions page Sect. 3.11, p141: 3.134, 3.138, 3.140	Sect. 3.11, 3.12, 4.1-4.3	Sect. 3.9, p135: book back right inside cover, 3.115, 3.117, 3.119, 3.121, 3.123, 3.125; challenge: 3.126, 3.127 Sect. 3.11, p141: 3.131, 3.133, 3.137, 3.141, 3.143
F 10/26 5pm, E1 Rm210	Sect. 4.2, p159: 4.4, 4.8, 4.12 Sect. 4.3, p164: 4.16, 4.20a, 4.24, 4.26 Sect. 4.4, p168: 4.30, 4.42 Sect. 4.5, p173: 4.46, 4.62, 4.64	4.4-4.7	Sect. 4.2, p159: 4.1, 4.3, 4.7, 4.11, 4.13 Sect. 4.3, p164: 4.15, 4.17, 4.19, 4.25, 4.27 Sect. 4.4, p168: 4.29, 4.31, 4.43, 4.45 Sect. 4.5, p173: 4.47, 4.53, 4.55, 4.59, 4.63, 4.65
M 11/12 3:15pm in class	Sect. 4.6, p180: 4.72, 4.86 Sect. 4.7, p185: 4.92 4.100 Sect. 4.9, p193: 4.104, 4.108, 4.112 Sect. 4.10, p196: 4.118 (see p10) Sect. 5.2, p218: 5.4, 5.6, 5.10	4.8-5.4	Sect. 4.6, p180: 4.67, 4.71, 4.75, 4.79, challenge: 4.89, 4.90 Sect. 4.7, p185: 4.91, 4.95, 4.97 Sect. 4.9, p193: 4.105, 4.106, 4.109, 4.113 Sect. 4.10, p196: 4.115, 4.117 Sect. 5.2, p218: 5.1, 5.3, 5.7, 5.9
F 11/16 5pm, E1 Rm210	Sect. 3.8, p129: 3.108 (assume Poisson distribution) Sect. 5.3, p229: 5.20, 5.22, 5.32 Sect. 5.4, p238: 5.42, 5.44, 5.30, 5.54, 5.56 Sect. 5.6, p247: 5.64, 5.72, 5.70 (assume y_1>0)	5.5-5.11	Sect. 3.8, p129: 3.97, 3.101, 3.107, 3.111, 3.114 Sect. 5.3, p229: 5.17, 5.19, 5.21, 5.23; challenge: 5.33, 5.35 Sect. 5.4, p238: 5.37, 5.39, 5.43, 5.45, 5.49, 5.53, 5.55, 5.57, 5.59, 5.61 Sect. 5.6, p247: 5.63, 5.65, 5.69; challenge: 5.73, 5.74
M 11/26 3:15pm, PH 108	WARNING: Answers only, or very little justification = no credit. I am assigning odd problems so you can have more feedback before the exam on 11/28. The solutions will be posted to these problems on 11/26; you can keep a photocopy of your homework to correct and study for the exam. Sect. 5.7, p253: 5.77, 5.81, 5.83 (read bottom half of p.250) Sect. 5.8, p261: 5.87, 5.91, 5.95 (use Tshebycheff) Sect. 6.3, p291: 6.3, 6.9 (average life=(Y1+Y2)/2), 6.11 Sect. 6.4, p300: 6.21, 6.27	6.1-6.5	Sect. 5.7, p253: 5.75, 5.79, 5.85 Sect. 5.8, p261: 5.86, 5.88, 5.89, 5.93, challenge: 5.97 Sect. 6.3, p291: 6.1, 6.5, 6.7, 6.13, 6.15; challenge: 6.17-6.18 Sect. 6.4, p300: 6.19, 6.23, 6.31, 6.32
W 12/5 3:15pm, PH 108	Final Homework. Pick up in office hours, 1-2pm, T/W Dec 11/12 Sect. 6.5, p307: 6.36, 6.40, 6.44 Sect. 6.6, p300: 6.54, 6.56 (Hint: for 6.54 use definition of gamma function, p176) Sect. 7.2, p342: 7.2(a-c), 7.4	6.6, 7.1-7.3 recommended but optional: 7.4-7.5	Sect. 6.5, p307: 6.35, 6.37, 6.41, 6.43, 6.45, 6.47, 6.49, 6.51 Sect. 6.6, p300: 6.53, 6.55, 6.57 Sect. 7.2, p342: 7.1, 7.3, 7.7, 7.11
Due Date	Problems to hand in	Reading	Recommended exercises

page maintained by Robert Ellis / http://math.iit.edu/~rellis/