# 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, Chebyshevâ€™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, Studentâ€™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

 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