♦ Definitions : Trial, Random and Non-random Experiment, Sample Point and Sample Space

♦ Definition of An Event and Different Types of Events : Complementary Event, Equally Likely Events, Certain Event, Impossible Event, Independent Events, Mutually Exclusive and Exhaustive Events

♦ Different Definitions of Probability : Classical (Mathematical), Empirical (Statistical) and Axiomatic Definitions of Probability

♦ Conditional Probability

♦ Theorems (Without Proof) and Their Applications :

i.Addition Theorem on Probability for Two and Three Events

ii.Multiplication Theorem on Probability for Two Events

iii.Bayes’ Theorem

Simple Examples Based on All Concepts.

♦ Random Variable : Discrete and Continuous Random Variables

Definition and Properties of Probability Mass Function. Cumulative Distribution Function.

♦ Expectation and Variance of a Random Variable. Theorems and Properties on Expectation and Variance of Random Variables Without Proof.

♦ Raw and Central Moments (Definition Only) and Their Relationship (Up to Order Four)

♦ Joint Probability Mass Function of Two Discrete Random Variables. Covariance.

♦ Correlation Analysis : Meaning, Types of Correlation

♦ Scatter Diagram, Product Moment or Karl Pearson’s Correlation Coefficient and Its Properties

♦ Spearman’s Rank Correlation (With and Without Ties)

♦ Concept of Linear Regression, Principle of Least Squares, Fitting of Regression Lines by Method of Least Squares

♦ Properties of Regression Equations

♦ Relation Between Regression Coefficients and Correlation Coefficient

♦ Concept and Use of Coefficient of Determination (R2)

♦ Introduction of Discrete Distributions – Discrete Uniform Distribution, Binomial Distribution, Poisson Distribution and Their Characteristics (Without Proof) Formulae and Their Interpretation