### Conduct of Course

This course will be conducted in flipped classroom blended mode in which lectures will not be delivered in conventional manner in physical classrooms; rather lectures will be available to students through videos that will be available online. Students can access these lectures online anytime, anywhere. Course content is divided into various modules. Each module deals with a single concept that is covered in one or more videos.  Students are expected to view these videos of their own before flipped classroom sessions which will be held in physical classrooms. In  flipped classrooms (one session of fifty minutes every week) students can discuss their doubts, problems or any concept related to the course. There will also be a problem solving tutorial session of fifty minutes every week where a tutor will physically solve some problems to explain some key concepts.  In addition to flipped classroom  and tutorial sessions, there will be one discussion session of fifty minutes every week where students who have lagged behind in flipped classrooms can further discuss their doubts related to lectures/tutorials. Tutorials and discussion sessions will also be conducted conventional way in physical classrooms.

### Release of Video Lectures

Every Friday/Saturday evening between four to six videos will be released. Total duration (per week) of these videos will be betwee 90-100 minutes (each video will be of about 10 to 35 minutes duration). Students are expected to view these videos of their own before coming to flipped classroom sessions.

### Course Content

Probability:- Axiomatic definition, properties, conditional probability, Bayes’ rule and independence of events. Random variables, distribution function, probability mass and density functions, expectation, moments, moment generating function, Chebyshev’s inequality. Special distributions; Bernoulli, binomial, geometric, negative binomial, hypergeometric, Poisson, exponential, gamma, Weibull, beta, Cauchy, double exponential, normal. Reliability and hazard rate, reliability of series and parallel systems. Joint distributions, marginal and conditional distributions, moments, independence of random variables, covariance and correlation. Functions of random variables. Weak Law of large numbers and Central limit theorems.

Statistics:- Descriptive statistics, graphical representation of the data, measures of location and variability. Population, sample, parameters.  Point estimation; method of moments, maximum likelihood estimator, unbiasedness, consistency. Confidence intervals for mean, difference of means, proportions.  Testing of hypothesis; Null and alternate hypothesis, Neyman Pearson fundamental lemma, Tests for one sample and two sample problems for normal populations, tests for proportions.

Text book: Introduction to Mathematical Statistics, Seventh Edition, by Robert V. Hogg, J. W. McKean, and Allen T. Craig, Pearson Education, Asia.

Although the policy of relative grading will be followed for awarding the final grades, there is a minimum performance requirement for each grade. These minimum performance requirements are given below: