Introduction to Probability & Statistics (in Hindi)

Overview

ABOUT THE COURSE:The course will cover topics in a standard syllabus in engineering degree programmes. But other students are also welcome to attend. Each concept in this introductory course will be illustrated with examples and reinforced with problems. By the end of the course, the student will have attained a fair degree of familiarity with basic statistical concepts of estimation and testing and would be well conversant with probabilistic concepts and standard probability distributions. The lectures will be in HINDI, with writing in English.INTENDED AUDIENCE: Undergraduate students. Also anyone who wants to get an introduction to statistical methods.PREREQUISITES: Calculus

Syllabus

Week 1: Introduction. Axiomatic definition and properties of probability.
Week 2:Conditional probability, Bayes' theorem. Independence of events.
Week 3:Random variables. Probability mass function and cumulative distributibution function for discrete random variables.
Week 4:

Expectation, variance, moments, moment generating function, Chebyshev's inequality.
Standard discrete distributions and their properties: Bernoulli, Binomial

Week 5:

Standard discrete distributions (continued): Geometric, Negative Binomial, Hypergeometric, Poisson.
Introduction to continuous random variables. Probability density function and cumulative distribution function of continuous random variables.

Week 6:

Expectation, variance moments, percentiles for continuous random variables.
Standard continuous distributions and properties: Uniform, Exponential, Gamma, Normal.

Week 7:Joint distributions, marginal and conditional distributions, moments, independence of random variables.
Week 8:Covariance, correlation. Central Limit theorem. Descriptive statistics, graphical representation of data
Week 9:

Measures of location and variability.
Introduction to Point estimation. Unbiased estimators, consistency.

Week 10:

Method of moments. Maximum likelihood estimation.
Confidence intervals for means and proportions.

Week 11:Testing of hypothesis: Null and Alternate hypothesis, Neyman Pearson lemma.
Week 12:Tests for one sample and two sample problems for normal populations. Tests for proportions. Large sample tests.