MTH 341 Probability Calendar Semester 091

Read assignments before class.  Review notes from previous classes regularly.

Number each exercise to the left.
Work only one problem across the page -- i.e. problems should proceed form top to bottom.
You must show your work! Correct mathematical notation must be used.  Partial credit is given when work is shown even if answer is incorrect. However, correct answers without any work shown will in general be given no credit.
If the problem is a computation leading to a final answer, box the answer.
Use pencil and eraser  -- do not scratch out work.

Start homework early and see me for help with problems you don't know how to work! It is inappropriate to ask how to do a problem in class the day it is due!!!! Staple your pages together before submitting.  My office is Core 257-- See my schedule for office hours or call or send email for an appointment. I am always delighted to help.

 

Date

Exams or Quizzes

 

Reading Assignments

Assignments Due --

 

Tentative – Will adjust as necessary

Mon.

8l/24

 

 

 

 

Wed.

 8/26

 

Section 1.2

Read section 1.1 for your own interest only.  In Section 1.2, we focus on learning terms and definitions and Venn Diagrams,   While a nice example of proof, you are not responsible for example 1.8 of section 1.2

 

Fri.
8/28

 

Sections 1.3, 1.4 

The three probability axioms and statements of the resulting three theorems in section 1.3 and   examples are important.   Results from section 1.4  (theorems and corollaries)  will be used over and over in this course!

 

Mon.
8/31

 

Sections  1.5, 1.6, 1.7

You may skip sections Section 1.5, 1.6 and 1.7 or read lightly – skipping formal arguments.  Know main points that I discuss in class about selecting points at random from an interval (uniform distribution). 

Set 1:  Section 1.2

Wed.
9/02

 

Sections 2.1, 2.2, 2.3

In Section 2.2 we are dealing with the counting principle ( the product rule for counting) with applications to some important examples.  Section 2.3 deals with permutations (ordered arrangements of objects)

 

Fri.
9/04

 

 

Section 2.4 deals with combinations (unordered selections of objects).

Set 2:  Section 1.4

Set 3:  Section 1.7 and Review ex.

Mon.
9/07

 

 

 

LABOR DAY NO CLASS

 

Wed.
9/09

 

Section 2.4

Section 3.1

Section 2.4 deals with combinations (unordered selections of objects).

In Section 3.1, look at the conditional probability of an event given that another event has occurred


Set 4:  Section 2.2

Fri.
9/11

 

 

Covers:  Def of Sample space, event, prob. Axioms, Principle of Inclusion Exclusion, Product Rule, Permutations, Combinations, Conditional Probability Formula

Set 5
Section 2.3

Mon.
9/14

 

 

 

Set 6:  Section 2.4

Wed.
9/16

 

Section 3.2

We rearrange the conditional probability formula to obtain the Law of Multiplication

Set 7:  Section 3.1

Fri.
9/18

Quiz

Section 3.3

The Law of Total Probability that allows us to calculate the probability of an event A using  P(A|B) and P(A|Bc).

 

Mon.
9/21

 

Section 3.4

Baye’s Formula

Set 8:  Section 3.2

Wed.
9/23

 

Section 3.5

Independence

Set 9: Section 3.3

Fri.
9/25

 

Section 4.1

Random Variable

Set 10:  Section 3.4

Mon.
9/28

 

 

 

 

Set 11:  Section 3.5

Wed.
9/30

Exam 1

 

 

 

Fri.
10/02

 

Section 4.1

Distribution function of a random variable

 

Mon.
10/05

 

Section 4.2

Defining concept of random variable  and its distribution function

 

Wed.
10/07

 

Section 4.3

Definition of a random variable's probability function.

Set 12:  Section 4.1, 4.2

Fri.
10/09

 

Section 4.4

Section 4.5

 

Expectation of a random variable.

Variance and Moments of random variables.

 

Mon.
10/12

 

Section 4.6

Section 5.1

Standardizing a random variable

Bernoulli and Binomial random variables; Binomials, calculating related probabilities, expected values and variances.

Set 13:  Section 4.3

Set 14:  Section 4.4

Wed.
10/14

Quiz  Topics

Section 5.2

Poisson random variable. Using it to approximate binomial random variables. Definition and properties of a Poisson process.  Probability function formula for Poisson random variable.

Set 15:  Section 4.5 and 4.6

Fri
10/16

 

 

NO CLASS -- MID TERM BREAK

 

Mon.
10/19

 

 

 

 

Wed.
10/21

 

Section 5.3

Other discrete random variables:  Geometric, hypergeometric, and negtive binomial random variables

Set 16:  Section 5.1

Fri.
10/23

 

 

 

Set 17: Section 5.2

Mon.
10/26

 

Section 6.1

Continuous random variables,  density function for continuous random variable. Relationship between density and distribution function.  Calculating various probabilities from each

Set 18:  Section 5.3

Wed.
10/28

 

 

 

 

Fri.
10/30

Exam 2

 

 

Set 19: Section 6.1

Mon.
11/02

 

Section 6.2

Through example 6.5.   Computing distribution function and density function of a function h(X) from the density of random variable X.

 

Wed.
11/04

 

Section 6.3

Computing expectation, variance and standard deviation of continuous random variables.

 

Fri.
11/06

 

Section 7.1

Uniform random variables

Set 20: Section 6.2

Mon.
11/09

 

Section 7.2

Normally distributed random variables;  approximation to binomial distribution.

Set 21: Section 6.3

Wed.
11/11

 

 

 

Set 22: Section 7.1

Fri.
11/13

 

Section 7.3

Exponential distribution. Density, relationship to a Poisson process

Set 23: Section 7.2

Mon.
11/16

 

 

 

 

Wed.
11/18

 

Section 8.1

Bivariate Distributions

Set 24: Section 7.3

Fri.
11/20

 

Sections 8.2

 

Independent Random Variables

Cancelled: Set 25: Section 7.4

Mon 11/23 – Fri 11/27

 

 

THANKSGIVING BREAK -- No Class

 

Mon.
11/30

 

Section 10.1

 Expectation of sums of random variables.   Indicator random variables.

Set 26: Section 8.1

Wed.
12/02

 

 

 

Set 27: Section 8.2

Fri.
12/04

Exam 3

 

 

Set 28 Section 10.1

Mon.
12/07

 

Sections 10.2, 10.3

 

Covariance and Correlation of jointly distributed random variables.   Variance of sums of independent random variables.

 

Wed.
12/09

 

Section 11.5

Central Limit Theorem  -- applications

Set 29: Section 10.9

Fri.
12/11

 

 

 

Set 30:  Section 11.5

Tues.
12/15

 

Final Exam
3:00 p.m.

 

 

 

Set Number

Written Problem Assignments

1

Section 1.2:  2, 5, 6, 7, 9, 10 -- draw Venn Diagrams for these also , 11

2

Section 1.4:  1, 2, 3, 4, 5, 6, 8,  12, 16, 18, 22, 26

3

Section 1.7 2, 4, 5, 10 and   Review Exercise 10, page 36.

4

Section 2.2  2, 4, 5, 6, 7, 8, 10, 15, 18

5

Section 2.3  1, 2, 4, 6, 9, 10, 12, 18, 21

6

Section 2.4  1, 2, 3, 4, 5, 6, 7, 15, 16, 18, 22

7

Section 3.1  2, 4,  7, 8, 9, 16

8

Section 3.2  2, 4, 6, 8

9

Section 3.3  1, 2, 3, 4, 6

10

Section 3.4  1, 2, 3, 6, 8

11

Section 3.5  1, 3, 4, 6, 8, 12, 15, 22

12

Section 4.2  1, 2, 5, 10, 11

13

Section 4.3  1, 2, 4, 7, 8

14

Section 4.4 2, 3,4, 5, 6

15

Section 4.5 1, 2, 4, 6, 7, 8; 
Section 4.6  2

16

Section 5.1:  1, 2, 6, 9, 10, 13, 18

17

Section 5.2:  1, 2, 4, 5, 6, 11, 12, 14, 16

18

Section 5.3:  1,  3, 4, 5, 8, 13, 16

19

Section 6.1:  1, 2, 5, 8

20

Section 6.2:  1, 2, 4,  5 

21

Section 6.3:  1, 2, 4, 8, 9

22

Section 7.1:  1, 2, 4, 5, 10

23

Section 7.2: 1, 2, 6, 8, 9, 10

24

Section 7.3  1, 2, 3, 4, 5, 7

25

Section 7.4  3, 5, 6

26

Section 8.1:  1, 2, 3, 6, 9;  

27

Section 8.2:  1, 2, 9, 11

28

Section 10.1:  4, 5, 12

29

Section 10.2:  2, 3, 18

Section 10.3  1, 2

30

Section 11.5:  1, 2, 3, 6