- Matrices Introduction
- Different Types of matrices
- Matrix algebra
- Addition, subtraction and multiplication of matrices
- Symmetric and skew Symmetric matrices
- Determinant of a matrix
- Inverse of a matrix
- Rank of a matrix
- Solution of Simultaneous linear equations using matrices
- Matrix inversion method
- Cramer’s rule
- Sets, Set Operations, Venn diagram
- Introduction and definition
- Different types of sets
- Union, intersection and complement of a set
- Difference of two sets
- Venn diagram
- Probability
- Definitions –random experiment, sample space events etc.
- Statement of Addition theorem and multiplication theorems
- Problems based on the above theorems
- Conditional probability
- Random Variable & Probability Distributions
- Discrete and continuous random variable
- Probability Distributions continuous and discrete
- Binomial distribution
- Poisson distribution
- Normal Distribution
- Uniform Distribution
- Problems based on the above
- Survey and sampling
- Population and universe
- Sampling
- Sample
- Types of Sampling
- Steps in sampling
- Test of Significance
- Introduction –Hypothesis testing
- Assumptions about parametric and non-parametric tests
- Hypothesis –Null and Alternate Hypothesis
- Hypothesis testing process
- Type 1 and Type 2 Errors
- Level of significance and rejection region
- Parametric Test
- Hypothesis test for the mean
- ANOVA
- Correlation and regression
- Regression –Introduction and definition
- Types of regression
- Line of best fit
- Regression equations
- Properties of regression lines and regression coefficients
- Standard error of estimate
- Simple linear regression
- Problems based on linear regression
- Correlation
- Introduction
- Types
- Coefficient of correlation
- Measurement of correlation
- Scatter Diagram
- Karl Pearson’s coefficient of correlation
- Rank correlation
- Coefficient of Variation
- Properties of correlation coefficient
- Decision Theory
- Decision analysis concept
- Types of decision making environment
- Decision making under certainty
- Decision making under un uncertainty
- Maximin, minimax, maximax, Laplace and Hurwitz alpha criterion
- Decision making under risk –EOL,EMV and EVPI criteria
- Decision trees
- Non Parametric Test
- Mann-Whitney U test
- Kolmogorov-Smirnov Z test
- Chi square test
- Time Series Analysis
- Introduction and definitions
- Various components of time series
- Determination of trend by
- Graphical method
- Moving average method
- Least Square method
- Calculation of seasonal indices
- Link relative method
- Descriptive statistics
- Measures of Central Tendency
- Advantages and disadvantages of– Mean, Median, Mode
- Operations Research
- Introduction and definitions
- Basic terms
- Phases of OR
- Linear programming –phases and definitions
- Linear Programming problems
- Introduction
- Formulation of LPP
- Transportation problem
- Introduction
- Mathematical Formulation
- Methods to find initial solution
- North west corner method
- Minimum cost method
- VAM
- Optimum solution
- Degeneracy in transportation problem
- Assignment problem
- Introduction
- Mathematical Formulation
- Solution
- Network model
- Critical path method
- Forward pass and backward pass
- Critical path, critical Activities
- Network model
- Crashing of project network
- Network model
- PERT(Project Evaluation and Review Technique)
- Queuing theory (Waiting line models)
- Queuing Theory –Introduction
- Components of Queuing model
- M/M/1: inf/FCFS Queuing model
- Problems
- Theory of games-Introduction
- Definitions-Pay off, Zero sum Game, Maximin, minimax criteria, saddle point etc.
- Solving games-Graphical method, algebraic method and Dominance method
- Simulation
- Simulation – Introduction and definitions
- Types of Simulation
- Monte –Carlo simulation
- Simulation of problems
- Probability
- Inverse Probability
- Bayes theorem and its applications in business
- Descriptive Statistics
- Measures of Dispersion
- Range
- Quartile Deviation
- Mean Deviation
- Standard deviation
- Variance