## CPA 1 SECTION 2 QUANTITATIVE ANALYSIS NOTES

** 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)

**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