CA43 Quantitative Analysis PDF notes

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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.

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

Emerging issues and trends


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