# Probability, Statistics and Stochastic Processes, January-May 2020

A slot

### Where and Who

 Roll Numbers Classroom Instructor Teaching Assistant BE, BS, CH, ED, MM, NA CRC $$305$$ Dr. Sivaram Ambikasaran Kandappan, MA16D300 CS CRC $$304$$ Dr. Sundar Nityananda Roy, MA16D018 ME18Bxyz where xyz $$\leq 120$$ CRC $$205$$ Dr. Sarang Sane Rohini S, MA17D017 AE, CE, EE, EP, PH, HS, Remaining ME CRC $$204$$ Dr. Dipramit Majumdar Pratiksha, MA17D004

### What

• Basic Probability
Axiomatic definition of probability, Conditional probability, Independent Events, Bayes' theorem, Counting

• Discrete Random Variables
Probability mass function, Cummulative distribution function, functions of random variables, expectation, mean, median, variance, Joint PMF, Conditioning, Independence

• Continuous Random Variables
Cummulative distribution function, Probability density function, functions of random variables, expectation, mean, median, variance, Joint PDF, Conditioning, Independence, normal random variables

• More on Random Variables
Derived distributions, Covariance and correlation, conditional expectation and variance, moment generating function, sums of random variables, Markov and Chebyshev inequality

• Limit theorems
Weak law of large numbers, Central limit theorem.

• Statistics
Sampling distribution, Estimation of parameters, Maximum likelihood estimates, Confidence intervals, Student’s t-distribution, Linear Regression, Hypothesis testing.

• Bernoulli and Poisson Processes
Introduction to Bernoulli and Poisson processes

• Markov Chains
Discrete-Time Markov Chains, Classification of states, Steady-State behavior, Absorption probabilities and expected time to absorption

• ### Problem Sets

Will be updated as and when the topics are covered.
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

### Textbooks

• Introduction to Probability, by Dimitri Bertsekas and John N. Tsitsiklis (referred as BT in Calendar)
• We will be omitting Chapter 8 and Sections 5.3, 5.5, 7.5.

### 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 M$$^2$$ in Calendar)
• Fundamentals of Applied Probability and Random Processes, by Oliver C. Ibe (referred as Ibe in Calendar)

The exam dates are tentative. Please check with the institute calendar.
 Evaluation Quiz-I Quiz-II EndSem Points 20 20 60 Date February $$17$$, Monday March $$30$$, Monday April $$29$$, Wednesday

### Lecture

Lecture summary

### Online material

#### March 30, Monday

• View lecture videos and the corresponding lecture slides: L18.1, L18.2, L18.3 from here
• Online quiz
• #### March 31, Tuesday

• View lecture videos and the corresponding lecture slides: L18.4, L18.5 from here
• Online quiz
• #### April 1, Wednesday

• View lecture videos and the corresponding lecture slides: L19.1, L19.2, L19.3, L19.4 from here
• Online quiz
• #### April 2, Thursday

• View lecture videos and the corresponding lecture slides: L19.5 from here
• Online quiz
• #### April 3, Friday

• View lecture videos and the corresponding lecture slides: L19.6 from here
• Online quiz
• #### April 6, Monday

• View lecture videos and the corresponding lecture slides: L19.7 from here
• Online quiz
• #### April 7, Tuesday

• View lecture videos and the corresponding lecture slides: L20.1, L20.2 from here
• #### April 8, Wednesday

• View lecture videos and the corresponding lecture slides: L20.3, L20.4 from here
• #### April 9, Thursday

• View lecture videos and the corresponding lecture slides: L20.5, L20.6 from here
• #### April 10, Friday

• View lecture videos and the corresponding lecture slides: L20.7, L20.8 from here
• #### April 13, Monday

• View lecture videos and the corresponding lecture slides: L20.9,L20.10 from here
• #### April 15, Wednesday

• View lecture videos and the corresponding lecture slides for Lecture 21
• Please note that the videos are from an earlier offering (Fall 2010) of the same course

#### April 16, Thursday

• View lecture videos and the corresponding lecture slides for Lecture 22
• Please note that the videos are from an earlier offering (Fall 2010) of the same course

#### April 17, Friday

• View lecture videos and the corresponding lecture slides for Lecture 23
• Please note that the videos are from an earlier offering (Fall 2010) of the same course

#### April 20, Monday

• View lecture videos and the corresponding lecture slides for Lecture 24
• Please note that the videos are from an earlier offering (Fall 2010) of the same course

#### April 21, Tuesday

• View lecture videos and the corresponding lecture slides for Lecture 25
• Please note that the videos are from an earlier offering (Fall 2010) of the same course

#### April 22, Wednesday

• View lecture videos and the corresponding lecture slides: L21.1, L21.2, L21.3, L21.4 from here
• #### April 23, Thursday

• View lecture videos and the corresponding lecture slides: L21.5, L21.6, L21.7 from here
• #### April 24, Friday

• View lecture videos and the corresponding lecture slides: L21.8, L21.9, L21.10 from here
• #### April 25, Saturday

• View lecture videos and the corresponding lecture slides: L22.1, L22.2, L22.3, L22.4 from here
• #### April 26, Sunday

• View lecture videos and the corresponding lecture slides: L22.5, L22.6, L22.7 from here
• #### April 27, Monday

• View lecture videos and the corresponding lecture slides: L22.8, L22.9, L22.10 from here
• #### April 28, Tuesday

• View lecture videos and the corresponding lecture slides: L24.1, L24.2, L24.3 from here
• #### April 29, Wednesday

• View lecture videos and the corresponding lecture slides: L24.4, L24.5 from here
• #### April 30, Thursday

• View lecture videos and the corresponding lecture slides: L24.6, L24.7, L24.8 from here
• #### May 1, Friday

• View lecture videos and the corresponding lecture slides: L25.1, L25.2, L25.3, L25.4, L25.5 from here
• #### May 2, Saturday

• View lecture videos and the corresponding lecture slides: L25.6, L25.7, L25.8, L25.9 from here

• Statistics online quiz

Random process and Markov Chain online quiz