Math 4710 – Fall 2019: Ross, A First Course in Probability ...

Math 4710 ? Fall 2019: Ross, A First Course in Probability (9th Edition), Tentative Outline

The course will be compatible with both the 8th and the 9th edition of the textbook. The homework problems coincide in both editions.

Week of

Section

8/29 and week of

9/2

9/9

9/16

9/23

1.1-1.6

2.2 2.3, 2.4

2.5 2.4, 2.5 3.1, 3.2

3.3 3.4 3.5

4.1

9/30

4.2

4.3, 4.4

10/7

4.5

4.6

10/14 10/21 10/28 11/4

4.7 4.8.1 4.8.2, 4.8.3 5.1 5.2

5.3, 5.4 5.5

5.6.1, 5.6.3 6.1 6.2

11/11

6.3 6.4, 6.5

11/18

11/25

12/2 and Mo 12/9

6.7 7.1, 7.2

7.4 7.5, 7.6

7.7 8.1, 8.2

8.3

Topics

Assignment numbers and due dates

Introduction, basic principle of counting, permutations, combinations, 1

binomial theorem, multinomial coefficients, integer solutions of equations

(Labor Day Monday)

Sample spaces and events

Axioms of probability, propositions about probabilities, inclusion-

2

exclusion principle

Equally likely outcomes: examples

Additional examples (inclusion-exclusion principle, arrangements

3

Conditional probabilities, multiplication rule

Bayes's formula

Independence of events, examples

4

Conditional independence

Random variables: introduction

5

Discrete random variables

Fri 10/4: First prelim (in class)

Expectation of a r.v. and examples

6

Variance of a r.v.

Bernoulli and binomial distribution

(Fall Break Monday)

7

Poisson distribution

Geometric distribution

Negative binomial and hypergeometric distributions

8

Continuous random variables: basic facts, density function

Continuous r.v.'s: expectation, variance

Uniform distribution and normal distribution

9

Exponential distribution

Gamma and Cauchy distribution

Joint distributions

10

Independent random variables

Sums of independent random variables

11

Conditional distributions

Fri 11/15: Second prelim (in class)

Functions of several random variables

12

Expectation and sums of random variables

Covariance and correlation of random variables

Conditional expectation, prediction

(Thanksgiving recess Wednesday, Friday)

Moment generating functions: definition, examples, properties

13

Limit theorems: Markov's inequality, Chebyshev's inequality, weak law of

large numbers

Central limit theorem

Ch.1, Pr: 20, 21, 22, 30 TE: 8, 9, 18 Wed 9/11

Ch.2, Pr: 2, 4, 9, 12; TE: 4, 5, 10 Wed 9/18 Ch.2, Pr: 23, 37, TE: 11, 16 Ch.3, Pr: 7, 11, TE: 1 Wed 9/25 Ch.3, Pr: 20, 33, 50, 53 TE: 4, 6, 9 Wed 10/2 Ch.3, Pr: 47, 81 (see hint on website), 84, TE: 12, 22 Wed 10/9 Ch.4, Pr: 21, 25, 28, 31 TE: 6, 7, 10 Wed 10/16 Ch.4, Pr: 38, 49, 57, 70 TE: 13, 16, 19 Wed 10/23 Ch.5, Pr: 7, 8, 11, 13 TE: 3, 5, 8 Wed 10/30 Ch.5, Pr: 18, 20, 23, 33 TE: 10, 13, 15 Wed 11/6 Ch.5, Pr: 36, 37, 39, 40 TE: 16, 20, 25 Wed 11/13 t.b.a Wed 11/20

t.b.a Wed 12/4

t.b.a Tue 12/10

Explanations on assignments: At the end of each chapter, the textbook gives different types of exercises: "Problems" (denoted Pr in the sequel), then "Theoretical exercises" (denoted TE here) and finally "Self-test problems and exercises". Each week 4 Pr problems (10 points each) and 3 TE questions (20 points each) will be assigned, so that in total each assignment will have 100 points. Solutions to many Pr problems are at the end of the book, but only in skeletal form (mostly as numbers) without any reasoning. In the homework, solutions must be properly explained and work must be shown.

Assignments may change! Check the course website for the actual assignments and due dates.

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