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**PAPER NO.12 QUANTITATIVE ANALYSIS GENERAL OBJECTIVE**

This paper is intended to equip the candidate with knowledge, skills and attitudes that will enable him/her to use quantitative analysis tools in business operations and decision making.

Table of Contents

- 1 LEARNING OUTCOMES
- 2 CONTENT
- 3 Matrix algebra
- 4 Calculus
- 5 Integration
- 6 Probability
- 7 Probability theory and distribution Probability theory
- 8 Probability distributions
- 9 Hypothesis testing and estimation
- 10 Correlation and regression analysis Correlation analysis
- 11 Time series
- 12 Linear programming
- 13 Decision theory
- 14 Game theory
- 15 Network planning and analysis
- 16 Queuing theory
- 17 Simulation

# LEARNING OUTCOMES

A candidate who passes this paper should be able to:

- Use mathematical techniques in solving business problems
- Apply set theory in business decision making
- Apply operation research techniques in decision making
- Apply simulation techniques in analysing business

# CONTENT

**Mathematical techniques****Functions**- Functions, equations and graphs: Linear, quadratic, cubic, exponential and logarithmic
- Application of mathematical functions in solving business problems

# Matrix algebra

- Types and operations (addition, subtraction, multiplication, transpositionand inversion)
- Application of matrices: statistical modelling, Markov analysis, input- output analysis and general applications

# Calculus

**Differentiation**

- Rules of differentiation (general rule, chain, product, quotient)
- Differentiation of exponential and logarithmic functions
- Higher order derivatives: turning points (maxima and minima)
- Ordinary derivatives and their applications
- Partial derivatives and their applications
- Constrained optimisation; lagrangian multiplier

# Integration

- Rules of integration
- Applications of integration to business problems

# Probability

**Set theory**- Types of sets
- Set description: enumeration and descriptive properties of sets
- Operations of sets: union, intersection, complement and difference
- Venn diagrams

# Probability theory and distribution Probability theory

- Definitions: event, outcome, experiment, sample space
- Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive

- Laws of probability: additive and multiplicative rules
- Baye’s Theorem
- Probability trees
- Expected value, variance, standard deviation and coefficient of variation using frequency and probability

# Probability distributions

- Discrete and continuous probability distributions (uniform, normal, binomial, poisson and exponential)
- Application of probability to business problems

# Hypothesis testing and estimation

- Hypothesis tests on the mean (when population standard deviation is unknown)
- Hypothesis tests on proportions
- Hypothesis tests on the difference between means (independent samples)
- Hypothesis tests on the difference between means (matched pairs)
- Hypothesis tests on the difference between two proportions

# Correlation and regression analysis Correlation analysis

- Scatter diagrams
- Measures of correlation –product moment and rank correlation coefficients (Pearson and Spearman)
- Regression analysis
- Simple and multiple linear regression analysis
- Assumptions of linear regression analysis
- Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics
- Computer output of linear regression
- T-ratios and confidence interval of the coefficients
- Analysis of Variances (ANOVA)

# Time series

- Definition of time series
- Components of time series (circular, seasonal, cyclical, irregular/ random, trend)
- Application of time series
- Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods
- Models – additive and multiplicative models
- Measurement of seasonal variation using additive and multiplicative models
- Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing
- Comparison and application of forecasts for different techniques
- Trend projection methods: linear, quadratic and exponential

# Linear programming

- Definition of decision variables, objective function and constraints
- Assumptions of linear programming
- Solving linear programming using graphical method
- Solving linear programming using simplex method
- Sensitivity analysis and economic meaning of shadow prices in business situations
- Interpretation of computer assisted solutions
- Transportation and assignment problems

# Decision theory

- Decision making process
- Decision making environment: deterministic situation (certainty)
- Decision making under risk – expected monetary value, expected opportunity loss, risk using coefficient of variation, expected value of perfect information
- Decision trees – sequential decision, expected value of sample information
- Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule

# Game theory

- Assumptions of game theory
- Zero sum games
- Pure strategy games (saddle point)
- Mixed strategy games (joint probability approach)
- Dominance, graphical reduction of a game
- Value of the game
- Non zero sum games
- Limitations of game theory

# Network planning and analysis

- Basic concepts – network, activity, event
- Activity sequencing and network diagram
- Critical path analysis (CPA)
- Float and its importance
- Crashing of activity/project completion time
- Project evaluation and review technique (PERT)
- Resource scheduling (leveling) and Gantt charts
- Advantages and limitations of CPA and PERT

# Queuing theory

- Components/elements of a queue: arrival rate, service rate, departure, customer behaviour, service discipline, finite and infinite queues, traffic intensity
- Elementary single server queuing systems
- Finite capacity queuing systems
- Multiple server queues

# Simulation

- Types of simulation
- Variables in a simulation model
- Construction of a simulation model
- Monte Carlo simulation
- Random numbers selection
- Simple queuing simulation: single server, single channel “first come first served” (FCFS) model
- Application of simulation models