Introduction to probability and Statistics

In today’s society, statistical thinking and technique are essential. Every discipline, including physical sciences, engineering and technology, economics, and social sciences, can benefit from it. Statistical methods are increasingly used in advanced research in electronics, electrical, computer science, industrial engineering, biology, genetics, and information science.

It is critical for pupils to become familiar with the subject of probability and statistics as early as possible. The purpose of this course is to introduce the subject to undergraduate and postgraduate science and engineering students.

probability and Statistics Course Outline

Week 01:Sets, Classes, and Collections | Sequence of Sets | Ring, Field (Algebra) | Sigma-Ring, Sigma-Field

Definitions of Probability | Monotone Class | Random Experiment

Conditional Probability | Event Independence | Probability Problems | Random Variables |

Week 02:A Random Variable’s Probability Distribution.

Week 03:A Random Variable’s Probability Distribution-II.

Week 04:Special Continuous Distributions | Poisson Process
Normal Distribution | Normal Distribution Problems | Random Variable Function

Week 05: Joint Distributions | Independence, Product Moments | Correlation and Linearity Property

Week 06 Bivariate Normal Distribution | Examples

Week 07:Basic Concepts | Chi-Square Distribution | Additive Properties of Distributions | Transformation of Random Variables | Distribution of Order Statistics | Basic Concepts|Chi-Square Distribution

Week 08:Chi-Square Distribution | t-Distribution | F-distribution | Descriptive Statistics

Week 09:Introduction to Estimation | Unbiased and Consistent Estimators | LSE, MME | MME, MLE Examples

Week 10: UMVUE, Sufficiency, Completeness | Rao-Blackwell Theorem and its Applications