# 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

### 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)

 Evaluation Quiz-I Quiz-II EndSem Points 20 20 60 Date February $$17$$, Monday March $$30$$, Monday April $$29$$, Wednesday