#### Topics

##### Mathematical Logic

##### Mathematical Logic

##### Matrices

- Determinant of a Matrix
- Types of Matrices
- Algebra of Matrices
- Properties of Matrices
- Elementary Transformations
- Inverse of Matrix
- Application of Matrices
- Properties of Transpose of a Matrix

##### Differentiation

- Derivatives of Composite Functions - Chain Rule
- Derivatives of Inverse Functions
- Derivatives of Logarithmic Functions
- Derivatives of Implicit Functions
- Derivatives of Parametric Functions
- Second Order Derivative

##### Applications of Derivatives

- Introduction of Derivatives
- Increasing and Decreasing Functions
- Maxima and Minima
- Application of Derivatives to Economics

##### Integration

##### Definite Integration

- Fundamental Theorem of Integral Calculus
- Properties of Definite Integrals

##### Applications of Definite Integration

- Standard Forms of Parabola and Their Shapes
- Standard Forms of Ellipse
- Area Under Simple Curves

##### Differential Equation and Applications

- Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equation by Eliminating Arbitary Constant
- Differential Equations with Variables Separable Method
- Homogeneous Differential Equations
- Linear Differential Equations
- Application of Differential Equations

##### Matrices

##### Commission, Brokerage and Discount

- Commission and Brokerage Agent
- Discount

##### Insurance and Annuity

- Concept of Insurance
- Fire Insurance
- Accident Insurance
- Marine Insurance
- Annuity

##### Linear Regression

- Regression
- Types of Linear Regression
- Fitting Simple Linear Regression
- The Method of Least Squares
- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Properties of Regression Coefficients

##### Time Series

- Introduction to Time Series
- Uses of Time Series Analysis
- Components of a Time Series
- Mathematical Models
- Measurement of Secular Trend

##### Index Numbers

- Index Numbers
- Types of Index Numbers
- Index Numbers - Terminology and Notation
- Construction of Index Numbers
- Simple Aggregate Method
- Weighted Aggregate Method
- Cost of Living Index Number
- Method of Constructing Cost of Living Index Numbers - Aggregative Expenditure Method
- Method of Constructing Cost of Living Index Numbers - Family Budget Method
- Uses of Cost of Living Index Number

##### Linear Programming

- Introduction of Linear Programming
- Linear Programming Problem (L.P.P.)
- Mathematical Formulation of Linear Programming Problem

##### Assignment Problem and Sequencing

- Assignment Problem
- Hungarian Method of Solving Assignment Problem
- Special Cases of Assignment Problem
- Sequencing Problem
- Types of Sequencing Problem
- Finding an Optimal Sequence

##### Probability Distributions

- Mean of a Random Variable
- Types of Random Variables
- Random Variables and Its Probability Distributions
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Binomial Distribution
- Bernoulli Trial
- Mean of Binomial Distribution (P.M.F.)
- Variance of Binomial Distribution (P.M.F.)
- Poisson Distribution
- Expected Value and Variance of a Random Variable

##### Continuity

##### Differentiation

##### Applications of Derivative

##### Indefinite Integration

- Definition of an Integral
- Integral of Standard Functions
- Rules of Integration
- Methods of Integration
- Integration by Parts

##### Definite Integrals

##### Ratio, Proportion and Partnership

##### Commission, Brokerage and Discount

##### Insurance and Annuity

- Insurance and Annuity

##### Demography

- Concept of Demography
- Uses of Vital Statistics in Demography
- Measurements of Mortality
- Life Tables

##### Bivariate Data and Correlation

##### Regression Analysis Introduction

- Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
- Regression Coefficient of X on Y and Y on X
- Regression Propertise

##### Random Variable and Probability Distribution

##### Management Mathematics

- Inequations in Management Mathematics
- Linear Programming Problem in Management Mathematics
- Assignment Problem
- Sequencing in Management Mathematics

## Definition

Let X be a random variable whose possible values `x_1, x_2, x_3, ..., x_n` occur with probabilities `p_1, p_2, p_3,..., p_n`, respectively. The mean of X, denoted by µ, is the number `sum_(i=1)^n x_i p_i` i.e. the mean of X is the weighted average of the possible values of X, each value being weighted by its probability with which it occurs.

The mean of a random variable X is also called the expectation of X, denoted by E(X).

Thus , E(X) = µ = `sum_(i = 1)^n x_ip_i = x_1p_1 + x_2p_2 + ... + x_np_n.`

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