# Probability, Statistics and Stochastic Processes, Jan-May 2024

### Note

If you want to register for this course, you will need to contact the Academic section. The instructors have no role/say in enrolling students for the class.

### Class time

The course is offered in 'A' slot, i.e., Monday @ 8AM, Tuesday @ 1PM, Thursday @ 11AM and Friday @ 10AM.

### Instructors and Branches

Instructor Branches Room
Dr. Vetrivel All CS CRC101
Dr. Sivaram CH+ED+EP+MM+NA CRC205
Dr. Dipramit ME 2022 till roll number ME22B180 CRC204
Dr. Barun AE+BE+BS+CE+EE+Remaining ME+PH+Rest CRC203

### 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 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 online lectures)

### Other Reference Textbooks

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

### Exams

Date and time of exam, check institute calendar.
Quiz - I Quiz - II Endsem
20 20 60

### Problem Sets

Problem Set 1 Problem Set 1 solution

Problem Set 2 Problem Set 2 solution

Problem Set 3 Problem Set 3 solution

Problem set 4 Problem set 4 solution

Problem set 5 Problem set 5 solution

Problem set 6 Problem set 6 solution part I Problem set 6 solution part II

Problem set 7 Problem set 7 solution

Problem set 8 Problem set 8 solution

### Other "random" stuff

George Burns on TV being interviewed on his 100th birthday: George Burns was puffing on a cigar and the interviewer made a comment about the negative correlation between longevity and smoking.
George Burns: "Twenty years ago my doctor told me that these cigars were going to kill me in the next five years with a probability of 99%"
Interviewer: "What does he say now?"
George Burns: "I don't know. He's dead"