KSh 550.00
Description
Page 2
CONTENT
1. Basic 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, transposition, and 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
– Integration
• Rules of integration
• Applications of integration to business problems
2. Probability
Set theory
– Types of sets
– Set description: Enumeration and descriptive properties of sets
– Operations of sets: Union, intersection, complement and difference
– Venn diagram
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
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)
QUANTITATIVE ANALYSIS
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– Hypothesis tests on the difference between two proportions
4. Correlation and regression analysis
Correlation analysis
• Scatter diagrams
• Measures of correlation –product moment and rank correlation coefficients (Pearson and
Spearman)
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)
• Simple and multiple linear regression analysis
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
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
7. Decision theory
– Decision process
– Decision making environment – deterministic situation (certainty), analytical hierarchical
approach (AHA), risk and uncertainty, stochastic situations (risk), situations of uncertainty
– Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision
rule, Laplace decision rule
– Decision making under risk – expected monetary value, expected opportunity loss,
minimising risk using coefficient of variation, expected value of perfect information
– Decision trees – sequential decision, expected value of sample information
– Limitations of expected monetary value criteria
QUANTITATIVE ANALYSIS
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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
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 (levelling) and Gantt charts
– Limitations and advantages of CPA and PERT
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
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. Current developments
– Role of advancement in information technology in solving quantitative analysis problems
13. Emerging issues and trends
