# 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"