# KASNEB NOTES – QUANTITATIVE ANALYSIS / QUANTITATIVE TECHNIQUES CONTENT COVERED

QUANTITATIVE ANALYSIS

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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.

12.0      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 situations.

CONTENT

12.1        Mathematical techniques

12.1.1  Functions

• Functions, equations and graphs: Linear, quadratic, cubic, exponential and logarithmic
• Application of mathematical functions in solving business problems

12.1.2 Matrix algebra

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

12.1.3 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

12.2      Probability

12.2.1 Set theory

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

12.2.2 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

12.3      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

12.4      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)

12.5    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

12.6      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

12.7      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

12.8      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

12.9     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

12.10   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

12.11   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

12.12   Emerging issues and trends

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