This is a course on theory of probability. In this course you will learn the nomenclature, theory and techniques needed for understanding the major types of probability problems, how to apply them in mathematical modeling, and how to prove problems in probability. We will cover materials including (not limited to) sample space, random variables, distribution functions, conditional probability and independence, expectation, combinatorial analysis, generating functions, convergence of random variables, characteristic functions, laws of large numbers, central limit theorem and its applications. This is a graduate course so you will have to learn how to prove problems (and you will be asked to prove problems).

**Probability and Statistics** Third Edition, DeGroot and Schervish.

Ruriko Yoshida, Assistant Professor of Statistics

- Office: 805A POT
- Phone: (859) 257-5698
- E-mail:
*ruriko.yoshida@uky.edu* - Office Hours: MW 10:00 AM - 11:00 AM

- MWF 12:00 PM - 12:50 PM, CB309

www.polytopes.net/courses/Stat524F07

We will cover Chapter 1, 2, 3, 4, and 5. For more details see PDF.

**Exam 1**Mon October 1.**Exam 2**Mon November 12.**Final**10:30 AM on Wed December 12. ROOM CB 309.

There will be two in-class exams, graded homeworks, and a final exam: these will count 40%, 30%, and 30% of your grade, respectively.

Students with excused absences will be given a make-up exam. No homework will be made up for credit, but it's important to make it up for your own benefit. The lowest scored HW will be discarded. Late homework will not be accepted. No make up final.

Write each problem neatly. If you have any question about grading, you must prove why you think so. Regrading will be in 7 days after returning. After 7 days, regrading will NOT be accepted. All exams will be in class. Calculator is allowed. They are closed book exams.

**Exam 1**October 1. Review on Chap 1 and 2 PDF. Practice Exam PDF. Solution PDF. Highest = 96, Mean = 71.071, STD = 14.715.**Exam 2**November 12. Review on Chap 3 and 4 PDF. Solution PDF. Highest = 100, Mean = 82.6, STD = 22.289.**Final**December 12.

Assignments will be weekly, handed out on
Friday and due back the next Friday. Typically these assignments
contain 5 or 6 regular problems.
assignments will be graded and returned and credits will be given **only** if an answer is completely correct. If you have an incorrect
answer, the problem will be returned to you with some hints and
you will be required to turn it in again with the next set of homework.
This will be repeated until the answer is correct.

**ALSOLUTELY NO LATE homework**.

The lowest homework score of each semester will be thrown out. This
is basically to handle those emergencies where you are unable to
complete an assignment for external reasons. I strongly recommend
you save this freebie as long as possible and do not blow off an
early assignment. MEAN = 77.468 out of 100, STD = 23.315.

- Homework 1 (PDF) Due: August 31st, Fri.
- Homework 2 (PDF) Due: September 7th, Fri.
- Homework 3 (PDF) Due: September 14th, Fri.
- Homework 4 (PDF) Due: September 21st, Fri.
- Homework 5 (PDF) Due: October 5th, Fri.
- Homework 6 (PDF) Due: October 12th, Fri.
- Homework 7 (PDF) Due: October 19th, Fri.
- Homework 8 (PDF) Due: October 29th, Mon.
- Homework 9 (PDF) Due: November 2nd, Fri.
- Homework 10 (PDF) Due: November 16th, Fri.
- Homework 11 (PDF) Due: November 30th, Fri. The last homework.

- Chapter 5 and Section 2.5 and 2.5 in the book.
- Finite Markov Chains and Algorithmic Applications, by Olle Haagstrom. London Mathematical Society, Student Texts 52, Cambridge University Press, 2002.
- Randomized Algorithms, by R. Motwani and P. Raghavan. Cambridge University Press, 1995.
- Algorithms for Random Generation and Counting - A Markov Chain Approach, by Alistair Sinclair. Birkhauser, 1993.
- Probability and Computing, by Michael Mitzenmacher and Eli Upfal. Cambridge University Press, 2005.
- Random Walks and Electrical Networks, by P. Doyle and J.L. Snell. Carus Mathematical Monograph no. 22, Mathematical Association of America, 1984. (Available on-line for free download.)
- Uniform Random Spanning Trees, by Robin Pemantle, in Topics in Contemporary Probability and Applications, Ed. J.L. Snell, CRC Press, 1995.
- Some New Games for your Computer, by Rick Durrett, in Topics in Contemporary Probability and Applications, Ed. J.L. Snell, CRC Press, 1995.
- Cellular Automata with Errors: Problems for Students of Probability, by Andrei Toom, in Topics in Contemporary Probability and Applications, Ed. J.L. Snell, CRC Press, 1995.
- How Many Times Should You Shuffle a Deck of Cards?, by Brad Mann, in Topics in Contemporary Probability and Applications, Ed. J.L. Snell, CRC Press, 1995.
- Random Graphs in Ecology, by Joel E. Cohen, in Topics in Contemporary Probability and Applications, Ed. J.L. Snell, CRC Press, 1995.
- A Matrix Perturbation View of the Small World Phenomenon, by D.J. Higham. SIAM J. Matrix Anal. Appl. 2003, Vol. 25, No. 2, pp. 429-444 (available on-line.)
- Random Graphs, by B. Bollobas. Academic Press, 1985.
- Stochastic Modelling for Systems Biology, by Darren J. Wilkinson. CRC, Mathematical and Computational Biology Series, 2006.
- Random Walks in Biology, by Howard C. Berg. Princeton U. Press, 1993.
- Computational Cell Biology, by C.P. Fall, E.S. Marland, J.M. Wagner, J.J. Tyson (editors). IAM volume 20 - Mathematical Biology, Springer-Verlag, 2002 (corrected third print, 2005).
- Branching processes in biology, by M. Kimmel and D.E. Axelrod. Springer, 2202.
- Evolutionary dynamics - exploring the equations of life, by M.A. Nowak. Belknap/Harvard, 2006.
- Stochastic Tools in Mathematics and Science, by A.J. Chorin and O.H. Hald. Springer, 2006.
- Theory and Applications of Stochastic Differential Equations, by Z. Schuss. John Wiley, 1980.
- Stochastic Differential Equations in Science and Engineering, by D. Henderson and P. Plaschko. World Scientific, 2006.
- Music and Probability, by David Temperley. MIT Press, 2007.
- Bayesian Methods for Music Signal Analysis, by A. Taylan Cemgil. (Look for PDF file on the web.)