# Introduction to Probability, Fall 2011

### Lecturer

### Scope

3cu.

### Lectures

*Week 37*:

Monday 9-12 and 15-18 in room B119

Tuesday 9-12 in room B321

Friday 9-12 and 15-18 in room CK111 and B321, respectively.

*Week 38*:

Monday 9-12 and 15-18 in room B119

Tuesday 9-12 in room B321

*Week 42*:

Monday 9-12 and 14-17 in room CK108 and CK107, respectively.

###### Notes

*Only the material of the weeks 37 and 38 will appear on the exam.

*Last session will be devoted to *your* questions and reviewing the key concepts.

### Prerequisites

Elementary Calculus

### Course Diary

12.09.2011: *1.Combinatorial Analysis;* Sections: 1, 2, 3, 4, 5.

12.09.2011: *2.Axioms of Probability;* Sections: 1, 2, 3, 4, 5, 6, 7.

13.09.2011: *3.Conditional Probability and Independence;* Sections: 1, 2, 3, 4, 5.

16.09.2011: *4.Random Variables;* Sections: 1, 2, 3, 4, 5.

16.09.2011: *4.Random Variables;* Sections: 6, 7, 8.1, 8.2, 8.3, 9.

19.09.2011: *5.Continuous Random Variables;* Sections: 1, 2, 3, 4.

19.09.2011: *5.Continuous Random Variables;* Sections: 5, 6.1, 6.2, 6.3, 6.4, 7.

20.09.2011: *6.Jointly Distributed Random Variables;* Sections: 1, 2, 4, 5.

17.10.2011: *8.Limit Theorems;* Sections: 1, 2, 3, 4. *10.Simulation;* Sections: 1, 2.1, 2.2, 3.

17.10.2011: *9.Additional Topics in Probability;* Section: 2.

### Self-Study Parts

Chapter 3: Examples 4f and 5f.

Chapter 4: 4.6.1.

Chapter 5: 5.4.1, 5.5.1.

Chapter 6: Examples 1f, 3e, 3f, 5c, and 5d.

###### Notes

*There will be one bonus question contributing to one point of the exam relating to these parts.

*Studying these parts will help you in doing the exercises.

### Exercises

Chapter 1: 21, 22, 23, 27, 2T, 5T, 8T, 9T, 13T.

Chapter 2: 15, 28, 56, 11T, 16T, 20T.

Chapter 3: 21, 35, 52, 59, 66, 69, 73, 15T, 22T, 30T.

Chapter 4: 26, 30, 31, 38, 43, 57, 80c, 4T, 8T, 9T, 10T, 13T, 19T, 27T, 28T.

Chapter 5: 3, 7, 10, 13, 18, 19, 21, 25, 26, 28, ,30, 31, 36, 38, 1T, 2T, 7T, 10T, 12T, 13T, 25T, 28T, 26T, 15T, 16T.

Chapter 6: 2, 8, 9, 13, 23, 24, 41, 39, 43, 51, 54, 12T, 14T, 20T, 19T.

### Solutions

chap-1.pdf

chap-2.pdf

chap-3.pdf

chap-4.pdf

chap-5.pdf

chap-6.pdf

###### Notes

*The 'T' indicates the Theoretical whereas the other numbers without suffixes are Problems.

*Solutions to the exercises should be handed in no later than 17.10.2011; 9:15 AM.

*Solutions to these exercises will be posted online after the due date of delivery.

*One can obtain one bonus point by solving at least 80 percent of the exercises i.e. 64 out of total of 80.

*Each group can hand in one set of solutions but students are strongly recommended to do all the exercises by themselves.

*There is no more than 10 percent exercises related to the self study parts i.e. 8 out of total of 80.

### Exams

Data: 24.10.2011.

Time: 10:00-13:00.

Place: Exactum, B120.

###### Notes

*The exam will contain six questions of which one bonus question is related to the self study parts.

*Each question is worth a point.

*You will *not* need a particular table or formula as they will be presented in the question if needed.

*There would be two separate exams on 17.11.2011 & 6.3.2012. If interested to take any of those , send me an email two weeks to the desirable date and also register for it in the Student Affair Office C329, two weeks prior to the exam.

*Your previous solutions to the exercises (if you handled in any) will not count toward your final grade if you take separate exam.

### Bibliography

Sheldon Ross, A First Course in Probability, Pearson, 2006.

### Type

NOTE. This course is for international Master´s degree program students. The course does not correspond or compensate the compulsory course "Johdatus todennäköisyyslaskentaan" in the degree requirements of mathematics and statistics.

### Registration

Did you forget to register? What to do.