Probability and Statistics

Overview

Instructor: Prof. Somesh Kumar, Department of Mathematics, IIT Kharagpur.

The use of statistical reasoning and methodology is indispensable in the modern world. It is true for any discipline, be it physical sciences, engineering and technology, economics or social sciences. Much of the advanced research in biology, genetics, and information science relies increasingly on the use of statistical tools. It is essential for the students to get acquainted with the subject of probability and statistics at an early stage. The present course has been designed to introduce the subject to undergraduate/postgraduate students in science and engineering. The course contains a good introduction to each topic and an advanced treatment of theory at a fairly understandable level to the students at this stage. Each concept has been explained through examples and application-oriented problems.

Syllabus

Mod-01 Lec-01 Algebra of Sets - I.
Mod-01 Lec-02 Algebra of Sets - II.
Mod-01 Lec-03 Introduction to Probability.
Mod-01 Lec-04 Laws of Probability - I.
Mod-01 Lec-05 Laws of Probability - II.
Mod-01 Lec-06 Problems in Proability.
Mod-01 Lec-07 Random Variables.
Mod-01 Lec-08 Probability Distributions.
Mod-01 Lec-09 Characteristics of Distributions.
Mod-01 Lec-10 Special Distributions - I.
Mod-01 Lec-11 Special Distributions - II.
Mod-01 Lec-12 Special Distributions - III.
Mod-01 Lec-13 Special Distributions - IV.
Mod-01 Lec-14 Special Distributions - V.
Mod-01 Lec-15 Special Distributions - VI.
Mod-01 Lec-16 Special Distributions - VII.
Mod-01 Lec-17 Function of a Random Variable.
Mod-01 Lec-18 Joint Distributions - I.
Mod-01Lec-19 Joint Distributions - II.
Mod-01 Lec-20 Joint Distributions - III.
Mod-01 Lec-21 Joint Distributions - IV.
Mod-01 Lec-22 Transformations of Random Vectors.
Mod-01 Lec-23 Sampling Distributions - I.
Mod-01 Lec-24 Sampling Distributions - II.
Mod-01 Lec-25 Descriptive Statistics - I.
Mod-01 Lec-26 Descriptive Statistics - II.
Mod-01 Lec-27 Estimation - I.
Mod-01 Lec-28 Estimation - II.
Mod-01 Lec-29 Estimation - III.
Mod-01 Lec-30 Estimation - IV.
Mod-01 Lec-31 Estimation - V.
Mod-01 Lec-32 Estimation - VI.
Mod-01 Lec-33 Testing of Hypothesis - I.
Mod-01 Lec-34 Testing of Hypothesis - II.
Mod-01 Lec-35 Testing of Hypothesis - III.
Mod-01 Lec-36 Testing of Hypothesis - IV.
Mod-01 Lec-37 Testing of Hypothesis - V.
Mod-01 Lec-38 Testing of Hypothesis - VI.
Mod-01 Lec-39 Testing of Hypothesis VII.
Mod-01 Lec-40 Testing of Hypothesis - VIII.