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• Introduction to probability with R, fall 2011

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# Introduction to Probability, Fall 2011

Ali Amiryousefi

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.

### 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

###### 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

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