# MSO201A: Probability and Statistics

## Course Description

This course will be conducted in flipped classroom mode in which typical lectures will not be delivered traditional way in physical classrooms; rather short lectures will be available to students through videos that will be available online. Generally each video will deal with a single concept. Students are expected to view these videos of their own before flipped classroom sessions which will be held in physical classrooms. In flipped classrooms (to be held in two sessions of fifty minute each) students can discuss their doubts, problems or any concept related to the course. In addition to flipped classroom sessions, there will be one problem solving tutorial session of fifty minute where tutor will solve some problems to explain certain key concepts. Tutorials will be conducted traditional way in physical classrooms.

## Release of Video Lectures

Every Friday evening between three to seven videos will be released. Total duration (per week) of these videos will be about 60 minutes (each video will be of about 10 to 20 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: