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# CA/CP43: QUANTITATIVE ANALYSIS

• Course level: Intermediate

#### Description

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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.

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

#### What Will I Learn?

• Mathematical techniques to solve business problems
• Application of set theory in business decision making
• Operation research techniques in decision making
• Use of simulation techniques in analysing business

86 Lessons120h

#### MATHEMATICAL TECHNIQUES – FUNCTIONS?

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

#### MATHEMATICAL TECHNIQUES – MATRIX ALGEBRA?

- Types and operations (addition, subtraction, multiplication, transposition and inversion) - Application of matrices: statistical modelling, Markov analysis, inputoutput 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

#### CALCULUS 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?

- 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 DISTRIBUTION?

- 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?

- 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

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### GlobopointConsultantsLtd

#### e-Learning Training and Consultation

Globopoint Consultants Limited is a fully registered Research, Training, and Consultancy firm based in Mombasa Kenya serving the entire East African region and beyond. The company is geared towards building professionals, entrepreneurs, growing businesses, and fostering sustainable economic development.

Globopoint Learning center is a fully accredited institution run by Globopoint Consultants Limited to specifically nurture modern-day professionals in the business field in an easy, practical, and convenient way.

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144 Courses

1409 students

KSh1,000.00

#### Material Includes

• Regularly updated online notes
• Handouts
• Zoom sessions
• Video Clips & Recordings
• KASNEB Past Papers Questions and Answers
• Case Studies

#### Target Audience

• CPA Section 4 Students
• CCP Section 4 Students
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