Probability, Statistics and Stochastic Processes, January-May 2020
When A slot
Where and Who
|BE, BS, CH, ED, MM, NA
||Dr. Sivaram Ambikasaran
||Nityananda Roy, MA16D018
|ME18Bxyz where xyz \(\leq 120\)
||Dr. Sarang Sane
||Rohini S, MA17D017
|AE, CE, EE, EP, PH, HS, Remaining ME
||Dr. Dipramit Majumdar
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
Weak law of large numbers, Central limit theorem.
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
Discrete-Time Markov Chains, Classification of states, Steady-State behavior, Absorption probabilities and expected time to absorption
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
- 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)
Grading and Exam schedule
The exam dates are tentative. Please check with the institute calendar.
||February \(17\), Monday
||March \(30\), Monday
||April \(29\), Wednesday
More details will be added later.