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Probability, Statistics and Stochastic Processes, January-May 2019
When Tuesday 1-2, Thursday 11-12, Friday 10-11; (Monday 8-9 will be used as a reserve slot)
Where Class Room Complex 305
Instructor
Sivaram Ambikasaran, 
Office: NAC 648
Problem Sets
Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
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
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)
Other Reference Textbooks
- 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 M2 in Calendar)
- Fundamentals of Applied Probability and Random Processes, by Oliver C. Ibe (referred as Ibe in Calendar)
Grading
| Evaluation |
Quiz-I |
Quiz-II |
EndSem |
| Points |
20 |
20 |
60 |
Quiz I will be on February 18, Monday.
Quiz II will be on March 25, Monday.
End Sem will be on April 29, Monday.
Calendar
Below is a very rough calendar, which will be updated as we progress through the course.
All the chapters are from BT unless indicated explicitly. Hypothesis testing will be covered from PLM.
From the book, we will be omitting Chapter 8 and Sections 5.3, 5.5, 7.5, 9.2, 9.3 and 9.4.
| Week |
Monday |
Tuesday |
Thursday |
Friday |
Practice problems |
| Jan 14- Jan 18 |
|
|
First class- Introduction |
Chapter 1, BT |
|
| Jan 21- Jan 25 |
No Class |
Chapter 1, BT |
Chapter 1, BT |
No Class |
|
| Jan 28- Feb 1 |
Chapter 1, BT |
Chapter 1, BT |
Chapter 2, BT |
Chapter 2, BT |
|
| Feb 4- Feb 8 |
No Class |
Chapter 2, BT |
Chapter 2, BT |
Chapter 2, BT |
|
| Feb 11- Feb 15 |
No Class |
Chapter 3, BT |
Chapter 3, BT |
Chapter 3, BT |
|
| Feb 18- Feb 22 |
QUIZ-I |
No Class |
No Class |
No Class |
|
| Feb 25- Mar 1 |
Chapter 3, BT |
Chapter 3, BT |
No Class |
Chapter 3, BT |
|
| Mar 4- Mar 8 |
Chapter 4, BT |
Chapter 4, BT |
Chapter 4, BT |
No Class |
|
| Mar 11- Mar 15 |
No Class |
Chapter 4, 5, BT |
Chapter 5, BT |
Chapter 5, BT |
|
| Mar 18- Mar 22 |
Chapter 5, 9, BT |
Section 9.1, BT |
|
Section 9.1, BT |
|
| Mar 25- Mar 29 |
QUIZ-II |
Section 9.1, BT |
Section 9.1, BT |
Hypothesis Testing, PLM |
|
| Apr 1- Apr 5 |
|
Hypothesis Testing, PLM |
Hypothesis Testing, PLM |
Chapter 6, BT |
|
| Apr 8- Apr 12 |
|
Chapter 6, BT |
Chapter 6, BT |
Finish Chapter 6, BT |
|
| Apr 15- Apr 19 |
Chapter 7, BT |
Chapter 7, BT |
Chapter 7, BT |
Holiday |
|
| Apr 22- Apr 26 |
|
Chapter 7 |
Chapter 7 |
Finish Chapter 7 |
|
| Apr 29- May 3 |
END SEM |
|
|
|
|
More details will be added later.