Probability, Statistics and Stochastic Processes, January-May 2020

When

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

    Textbooks

    Other Reference Textbooks

    Grading and Exam schedule

    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 summary

    Lecture summary

    More details will be added later.