# Probability, Statistics and Stochastic Processes, January-May 2018

When Tuesday 1-2, Thursday 11-12, Friday 10-11; (Monday 8-9 will be used as a reserve slot)
Where Class Room Complex 304

### Instructor

Sivaram Ambikasaran,
Office: HSB 241C
Office hours: 9:30 AM to 11:30 AM, Mondays.

### Syllabus

Probability Axiomatic definition of probability, Independent Events, Baye's theorem, Discrete and continuous random variables, Distribution, Functions of random variables, Expectation, Variance, Correlation coefficient, Chebyshev’s inequality, Markov inequality, Conditional expectations, Standard discrete and continuous distributions (Binomial, Poisson, Geometric, Exponential, Normal, Chi-square), Moment generating function, Sums of random variables, Law of large numbers, Central limit theorem, Normal approximation to Binomial.
Statistics Sampling distribution, Estimation of parameters, Maximum likelihood estimates, Confidence intervals, Student’s t-distribution, Testing hypothesis, Goodness of fit.
Stochastic Processes Continuous and discrete random process, Stationary random process, Bernoulli process, Poisson process, Markov chain.

### Textbooks

• Introduction to Probability, by Dimitri Bertsekas and John N. Tsitsiklis (referred as BT in Calendar)
• Introductory Probability and Statistical Applications, by Paul L. Meyer (referred as PLM in Calendar)
• John E. Freund's Mathematical Statistics with Applications, by Irwin Miller and Marylees Miller (referred as M$$^2$$ in Calendar)
• Fundamentals of Applied Probability and Random Processes, by Oliver C. Ibe (referred as Ibe in Calendar)

### Other Reference Textbooks

• Introduction to Probability Models, by Sheldon M. Ross

### Grading

 Evaluation Quiz-I Quiz-II EndSem Points 20 20 60

Quiz I will be on February $$19$$, Monday.

Quiz II will be on April $$2$$, Monday.

End Sem will be on May $$1$$, Tuesday.

### Calendar

Below is a very rough calendar, which will be updated as we progress through the course.
 Week Monday Tuesday Thursday Friday Practice problems Jan 15- Jan 19 Chapter 1 from BT Chapter 1 from BT Chapter 1 from BT Chapter $$1$$ practice problems Solutions Jan 22- Jan 26 Jan 29- Feb 2 Chapter 1 from BT Chapter 2 from BT Chapter 2 from BT Feb 5- Feb 9 Chapter 2 from BT Chapter 2 from BT Chapter 2 from BT Chapter $$2$$ practice problems Feb 12- Feb 16 Chapter 2,3 from BT Chapter 3 from BT Chapter 3 from BT Chapter 3 from BT Feb 19- Feb 23 Quiz I Chapter 3.4 from BT Chapter 3.5 from BT Chapter 4.1 from BT Feb 26- Mar 2 Chapter 4.2 from BT Mar 5- Mar 9 Chapter 10 from PLM Chapter 10 from PLM Chapter 5 from BT/ Chapter 12 from PLM Mar 12- Mar 16 Chapter 5 from BT/ Chapter 12 from PLM Chapter 5 from BT/ Chapter 12 from PLM Chapter 13 from PLM Chapter 13 from PLM Mar 19- Mar 23 Chapter 13 from PLM Chapter 14 from PLM Chapter 14 from PLM Chapter 14 from PLM Mar 26- Mar 30 Chapter 14 from PLM Practice problems Apr 2- Apr 6 Quiz II Chapter 15 from PLM Chapter 15 from PLM Apr 9- Apr 13 Chapter 6.1 from BT Apr 16- Apr 20 Chapter 6.2 from BT Chapter 6.2 from BT Chapter 7.1 from BT Apr 23- Apr 27 Chapter 7.2 from BT Chapter 7.3 from BT Chapter 7.3 from BT Review Apr 30- May 4 End Sem