MATH 3355 Probability

Final     Remarks

Homework Assignments

Assigned from Ghahramani, Fundamentals of Probability, Third Edition.
Assigned
Section
 ProblemsNotes
5/4 10.1
11.2
11.5		 4, 13, 14
6, 7, 10, 16
1, 3, 6, 8		  
read this section (skip the proofs)
read this section (skip the proofs)
4/29 9.1 2, 3, 7, 24 (and 25 if you're interested) read this section and section 10.1 (through page 407)
4/27 8.3 2 - 5, 7, 8 read this section
  7.3
7.4
8.1
8.2		 1, 4, 5, 7, 8
1 - 4
1 - 13 odd
1 - 7 odd, 11, 12, 17, 18		 read these sections
3/24 6.2
6.3
7.1
7.2		 1, 3, 5
2, 4, 5, 7, 8
1, 2, 3, 5, 7, 10
1, 2, 28, 29		 read these sections
3/18 6.1 1, 3 - 6, 8 - 10 read this section
3/16 5.2
5.3		 1 - 3, 5 - 7, 11, 15, 16
1 - 3, 5 - 7, 15, 16		 read these sections
3/9 4.5
4.6
5.1		 1 - 8
1
as many of 1 - 20 as you need		 read these sections
3/2 4.3
4.4		 1 - 5, 7 - 10, 13 (Y is a consonant), 14
2, 3, 5, 6, 8, 10, 12, 13, 16		 read these sections
2/18 4.2 1 - 7, 10, 11 read section 4.1 and 4.2
2/11 3.5 2, 4 - 7, 12 - 17, 24, 31, 34 read this section
2/9 3.2
3.3
3.4		 1 - 5
1, 4, 8
2, 3, 5, 8		 read these sections
2/4 3.1 1 - 6, 9, 11, 16, 17, 19, 21 read section 3.1
2/4 2.4 1, 3, 4, 6, 7, 11, 13, 15, 21, 25, 39 read sections 2.4 and 2.5
1/28 2.3 2 - 4, 8 - 13, 17, 18, 23
1/28 2.2 1, 2, 4, 7, 11, 14, 15, 23, 25, 27 read sections 2.1 through 2.3
1/26 1.7 1 - 5, 7, 8, 10 read sections 1.5 through 1.7
1/19 1.4 1 - 13 odd, 14, 15, 19 read sections 1.3 and 1.4
1/19 1.2 1 - 13 odd, 16 read sections 1.1 and 1.2

Exam 1     Answers

Exam 1 will take place on Thursday, February 25. It will cover material we've discussed from Chapters 1 - 3 and the beginning of Chapter 4 (through section 4.2) in the text. If you have questions regarding this material that you'd like to discuss, be prepared to ask them in class on Tuesday, February 23. You may also make use of my office hours.
I will expect you to have a good working understanding of the concepts we've discussed, and to be able to use them in problems such as those discussed in class and those that appear in the homework and WeBWorK assignments. These concepts should be pretty clear. Paraphrasing some of the titles of the relevant sections of the text:
    Sample Spaces and Events; Axioms of Probability; Basic Properties; Random Selection of Points;
    Counting Principle; Permutations; Combinations (binomial and multinomial coefficients/expansion);
    Conditional Probability; Multiplication Law; Total Probability Law; Bayes' Formula; Independence;
    Random Variables; Distribution Functions
Some potentially relevant review problems from the ends of the chapters (in the 3rd edition of the text):
Chapter 1 (page 35): #1 - 9, 11, 13, 15
Chapter 2 (page 71): #1 - 11, 17-19
Chapter 3 (page 136): #1 - 5, 7 - 11, 17
Chapter 4 (page 186): #4, 6, 8
Solutions to the odd numbered problems may be found in the back of the text.
You may also find the homework and WebWorK assignments useful for studying.

Exam 2     Answers

Exam 2 will take place on Thursday, April 1. It will cover the material we've discussed from Chapters 4 - 7 in the text (since Exam 1). If you have questions regarding this material that you'd like to discuss, be prepared to ask them in class on Tuesday, March 30. You may also make use of my office hours.
As before, I will expect you to have a good working understanding of the concepts we've discussed, and to be able to use them in problems such as those discussed in class and those that appear in the homework and WeBWorK assignments.
Virtually everything we've discussed since the first exam has involved random variables. Know what they are and how to identify them in word problems. Understand probability mass and density functions (in the discrete and continuous cases respectively), as well as distribution functions and how to compute probabilities using them. Know what expectation, variance, and standard deviation are, and how to compute them. Also, be able to compute expectations, etc. of functions of random variables.
We've discussed a number of specific types of discrete and continuous random variables, including binomial (with Bernoulli as a special case), Poisson, geometric, negative binomial, uniform, and (standard) normal. Know or be able to quickly derive their expectations and variances. It is important that you are able to identify which random variable is relevant for a given problem, and are able to use this indentification to solve the problem. Also, be aware that some problems do not fit into any of the standard models, and must be done by hand.
Poisson and (standard) normal RVs are often used to approximate binomial RVs when the number of trials is large. Be prepared to use these approximations. Only one will be applicable in a given problem. Know which one to use, and how to use it. In particular, don't forget about the correction for continuity in the (standard) normal case. I will provide a table for use in problems involving (standard) normal RVs.
Some potentially relevant review problems from the ends of the chapters (in the 3rd edition of the text):
Chapter 4 (page 185): #1, 5, 7, 9 (4, 6, 8 were suggested prior to Exam 1)
Chapter 5 (page 228): #1, 3, 5, 7, 11, 15, 21
Chapter 6 (page 258): #1, 5, 6, 7, 11
Chapter 7 (page 308): #1, 3
Solutions to the odd numbered problems may be found in the back of the text.
You may also find the homework and WebWorK assignments useful for studying.

Dan Cohen   Spring 2010     Back to MATH 3355-3; to my homepage.