### Degree Type:

Bachelor of Science### Department:

Department of Statistics### Modes of Study:

Regular### About Programme:

In today’s increasingly complicated international business world, a strong preparation in the fundamentals of both economics and mathematics is crucial to success. Graduates can find work as economists, market research analysts, financial analysts, and financial planners, amongst several other rewarding career fields.

### Entry Requirements:

Applicants must obtain passes in Elective Mathematics and any two (2) of the following elective subjects: Physics, Chemistry, Economics, Biology and Technical Drawing.** **The minimum admission requirement into the University of Cape Coast for WASSCE applicants is aggregate 36. For SSSCE applicants, the minimum requirement is aggregate 24. NOTE For purposes of admission, a pass in (i) WASSCE means Grade: A1 – C6 (ii) SSSCE means Grade: A – D.

### Career Opportunities:

This programme combines the main contents of both economics and mathematics within a programmatic structure that joins the two disciplines. It applies mathematical methods to represent theories and analyse problems in economics. It is argued that mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects. In addition, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without it. Therefore a combination of both disciplines in a single programme ensures that our graduates enter the world of work with the requisite skills.

## Programme Structure

### Level 100

### First Semester

## CMS 107: Communicative Skills I

Engaging in academic work at the university is challenging. This course is aimed at equipping fresh students to make the transition from pre-university level to the university level. It assists them in engaging and succeeding in complex academic tasks in speaking, listening, reading and writing. It also provides an introduction to university studies by equipping students with skills that will help them to engage in academic discourse with confidence and fluency.

## STA 101: INTRODUCTION TO PROBABILITY

The course is a general introduction to preliminary concepts in probability: definitions – sample space, events, etc.; permutation and combination. Concept of probability:

probability measure ― axioms; joint, marginal and conditional probability; Independence; total probability; Bayes’ theorem. Random variable and probability distribution:

probability distribution of a random variable (discrete and continuous)

### Second Semester

## CMS 108: Communicative Skills II

This is a follow-up course on the first semester one. It takes students through writing correct sentences, devoid of ambiguity, through the paragraph and its appropriate development to the fully-developed essay. The course also emphasizes the importance and the processes of editing written work.

## STA 102: INTRODUCTION TO STATISTICS

A general introduction to Statistics and statistical data: Introduction ― branches of statistics; types of statistics, e.g., Official Statistics: Health, Industry, etc.; types of data ― categorical data and their representations; Proportions. Descriptive statistics: representations of data ― diagrams and tables; measures of central tendency; types of means; measures of dispersion; measures of skewness and peakedness; diagrammatic representations.

### Level 200

### First Semester

## STA 203: FURTHER PROBABILITY

Distribution function of a random variable; expectation and variance of a random variable; probability distributions ― Binomial, Negative Binomial, Geometric, Hypergeometric, Poisson, Normal, Exponential (Exclude Beta and Gamma Distributions). Moment generating functions: moments of a random variable (e.g., Binomial, Poisson, etc.); moment generating function of a random variable; some applications. Bivariate distributions: bivariate random variable; joint, marginal and conditional distributions; statistical independence; conditional expectations and variance; regression function.

### Second Semester

## STA 202: FURTHER STATISTICS

Types of survey, e.g., household, demographic, health, etc. Planning of surveys-objective; target populations; questionnaire design; pilot survey. Regression and correlation analysis: methods for simple linear regression ― graphical method, method of least squares (with derivation); interpretation of coefficients; simple coefficient of determination; correlation coefficient; standard error of estimate. Rank order correlation analysis: introduction to rank correlation; Spearman’s coefficient; Kendall’s coefficient.

### Level 300

### First Semester

## STA 301: PROBABILITY DISTRIBUTIONS

Further distribution concepts: Application of conditional expectation and variance, a random number of a random variable; sampling distribution of a statistic; Poisson distribution and Poisson processes; multinomial experiments. Transformation of random variables: Functions of one-dimensional random variables; the convolution theorem; distribution of a function of a random variable; Jacobian transformation; function of bivariate random variable; some applications – the Beta-distribution family; the Gamma, Chi-square, *t *– and *F* – distributions. Generating functions: characteristic functions; moment generating function of Beta and Gamma random variables; moment generating function of a function of a random variable; probability generating functions; some applications. Limiting Distributions: Limiting distribution function of a random variable (with proofs); the central limit theorem; law of large numbers; some applications – limiting form of the Binomial distribution; approximation to the Poisson distribution. Concepts of convergence: convergence in probability; convergence in mean square; Chebyshev inequality.

## STA 303: STATISTICAL METHODS I

Theory of hypothesis testing-likelihood ratio tests; power functions, etc; tests concerning means; differences between means; variances; proportions. Test for associations (contingency tables) and goodness of fit tests. Standard assumptions and their plausibility in hypothesis testing. Linear regression analysis ― the method of least squares (derivation of normal equations); prediction and confidence intervals; regression diagnostics. One-and two way analysis of variance.

## STA 305: DESIGN AND ANALYSIS OF EXPERIMENTS

Basic concepts/terminologies – e.g., units, treatments, factors. Completely randomized designs. Randomized block designs-efficiency, missing data. Latin squares. Sensitivity of randomized block and Latin square experiment. Factorial experiments-several factors at two levels; effects and interactions; complete and partial confounding of factorial experiments. Split-plot experiments-efficiency; missing data; split-plot confounding.

## STA 399: RESEARCH METHODS

Sources of information. Report writing: Structure – title, summary, introduction, results, conclusions, recommendations, methods, general discussion, references, appendices;

Content; Presentation; Style. Oral presentation: Preparation – logistical requirements, e.g., Flip charts, transparencies, overhead projector, slides, etc. Delivery – use of Power Point software;

Introduction to proposal writing.

### Second Semester

## STA 302: SAMPLING TECHNIQUES AND SURVEY METHODS

This course will introduce students to the sampling methods. The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size; estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc. Stratified random sampling - proportional and optimum allocations. Cluster sampling, systematic sampling, multistage sampling.

## STA 304: DATA ANALYSIS I

Introduction to Statistical Software: Eg. SPSS, Minitab, R, Matlab. Statistical data – Data from designed experiments; sample surveys; observational studies. Data exploration - sample descriptive techniques: measures of location and spread; correlation, etc. Diagrammatic representation of data: the histogram; stem - and leaf -; box-plot; charts, etc. Tabulation, interpretation of summary statistics and diagrams. Regression and Correlation Analysis: Simple Linear Regression. Interpretation of coefficients, Correlation and coefficient of determination. One-way ANOVA.

## STA 306: MULTIVARIATE DISTRIBUTIONS

Vector random variables: expected values of random vectors and matrices; covariance matrices; linear transforms of random vectors; further properties of the covariance matrix; singular and non-singular distributions; quadratic functions of random vectors. Distribution concepts: distribution of a random vector; multivariate moment generating functions. Transformation of random variables: vector transformation and Jacobian; change of variables in multiple integrals; distribution of functions of random vectors; some applications – the Beta-distribution family; the Chi-square, *t *– and *F* – distributions. Order statistics: order transformation; joint distributions of order statistics; marginal distributions; alternative methods. Multivariate normal distribution: definition and examples; singular and non-singular distributions; properties of the multivariate normal distribution; multivariate normal density; independence of multivariate normal vectors. Conditional distribution:

## STA 308: SAMPLING TECHNIQUES

This course will introduce students to the sampling methods. The areas to cover include: Simple random sampling (with or without replacement)-estimation of sample size;

estimation of population parameters e.g., total and proportion; ratio estimators of population means, totals, etc. Stratified random sampling - proportional and optimum allocations.

Cluster sampling, systematic sampling, multistage sampling.

### Level 400

### First Semester

## STA 401: DATA ANALYSIS II

Report writing and presentation ― organization, structure, contents and style of report. Preparing reports for oral presentation. Introduction to word processing packages, e.g., word for windows and latex. Single- and two-sample problems; Poisson and binomial models. Introduction to the use of generalized linear modeling in the analysis of binary data and contingency tables. Simple and multiple linear regression methods; dummy variables; model diagnostics; one and two-way analysis of variance. Data exploration method - summary and graphical displays. Simple problems in forecasting.

## STA 403: STATISTICAL METHODS II

Further methods for discrete data: examples and formulation - binomial, multinomial and Poisson distributions. Comparison of two binomials; McNeyman’s test for matched pairs; theory and transformations of variables; multiple linear regression; selection of variables ; use of dummy variables. Introduction to logistic regression and generalized linear modeling. Non-parametric methods. Use of least squares principle; estimation of contrasts, two-way crossed classified data.

## STA 404: INTRODUCTION TO STOCHASTIC PROCESSES

Preliminary concepts: the nature of a stochastic process, parameter space and state space. Markov processes and Markov chains. Renewal processes. Stationary processes. Markov chains: First order and higher order transition probabilities. Direct computation for two-state Markov chains. The Chapman-Kolmogorov equations. Unconditional state probabilities. Limiting distribution of a two-state chain. Classification of states. Closed sets and irreducible chains. Various criteria for classification of states. Queuing processes: characteristics and examples. Differential equations for a generalised queuing model. M/M/1 and M/M/S queues: characteristics of queue length, serving times and waiting time distributions. Inter-arrival times and traffic intensity. Applications to traffic flow and other congestion problems.

## STA 405: MULTIVARIATE METHODS

The course is specifically designed to introduce students to multivariate techniques. It helps students to handle multivariate data effectively. Specific areas include: Structure of multivariate data. Inferences about multivariate means - Hotelling’s ; likelihood ratio tests, etc. Comparisons of several multivariate means - paired comparisons; one-way MANOVA; profile analysis. Principal component analysis - graphing; summarizing sample variation, etc. Factor analysis. Discriminant analysis - separation and classification for two populations; Fisher’s discriminant function; Fisher’s method for discriminating among several populations Cluster analysis - hierarchical clustering; non-hierarchical clustering; multi-dimensional scaling.

## STA 406: TIME SERIES ANALYSIS

Stationary and non-stationary of series: removal of trend and seasonality by differencing. Moments and auto-correlation. Models: simple AR and MA models (mainly AR(1), MA(1)): moments and auto-correlations; the conditions of stationarity: invertibility. Mixed (ARMA) models, and the AR representation of MA and ARMA models. Yule-Walker equations and partial auto-correlations (showing forms for simple AR, MA models). Examples showing simulated series from such processes, and sample auto-correlations and partial auto-correlations.

## STA 409: ECONOMIC AND SOCIAL STATISTICS

Nature, scope and sources of social and economic statistics: industrial statistics; trade statistics; financial statistics; price statistics and demographic statistics. assessing social development and living standards - social indicators, e.g., education, occupation, sex, etc; economic indices - real income; cost of income; cost of living, and price indices. National income accounting - gross national product; gross domestic product. The UN system of National accounting. Methods of estimation-income approach; production approach; expenditure approach. National accounts - personal sector; production sector; government sector and international sector. National income trends short and long-term changes. Input-output analysis-construction of transaction matrix in quantitative and monetary values. Input matrix-interpretation of technical coefficients. The technology matrix - interpretation of interdependence coefficients; multiplier analysis and price effects; consistent method and impact analysis. Analysis of input-output tables - open and closed models; derivation and solution of input-output equations.

## STA 413: STATISTICAL INFERENCE

Estimation theory - unbiased estimators; efficiency; consistency; sufficiency; robustness. The method of moments. The method of maximum likelihood. Bayesian estimation - prior and posterior distributions; Bayes’ theorem; Bayesian significant testing and confidence intervals. Applications - point and intervals. Estimations of means, variances, differences between means, etc. Hypothesis testing theory - test functions; the Neyman - Pearson Lemma; the power function of tests, Likelihood ratio test.

## STA 415: DEMOGRAPHY

Conventional and adjusted measures of mortality, measures of fertility, measures of morbidity. Demographic characteristics and trends of selected countries.

Evaluation of demographic data. Projections for stable and stationary populations. Actuarial applications of demographic characteristics and trends.

### Second Semester

## STA 410: ACTUARIAL STATISTICS

Principles of General Insurance. Theory of Interest and Decremental Rates. Life Contingencies, Social Security and Pension Schemes. Risk Analysis and associated statistical problems. General Insurance Principles: The Economics of Insurance. The Risk elements. General concepts and practices; Contingency, Risk, Exposure, Premium. Portfolio, Claims. The Theory of Interest Rates: Basic Compound interest Functions. Equations of Value. Effective Rates of Interest, and Force of Interest. Annuities Certain. Increasing and decreasing annuities Perpetuities. Life Contingencies: Single-Life Annuities and Assurances. The determination of values and premiums. Construction of Mortality, Sickness, Multiple decrement and similar tables from graduated data. Determination and Use of probability and monetary Functions based on such tables. Survival Probabilities and Expectation of Life. Mortality: Mortality Rates and other Indices. Analysis of Experience Data. Calculation of mortality and other decremental rates (including multiple decrement rates). Relevant Demographic Statistics: Evaluation of demographic data and their application to actuarial work. Population projections. Demographic characteristics in Ghana.

## STA 412: STATISTICS IN MEDICINE

Organisation and Planning: Protocol, patient selection, response. Justification of method for randomisation: Uncontrolled trials, blind trials, Placebo’s, ethical issues. Survival function, hazard functions, cumulative hazard function, censoring. Kaplan-Meier survival curve, parametric models. Dynamics of isolated and interacting populations, cobwebbing. The basic laws of genetics. Mutation. Inherited defects in man.

### Level 800

### First Semester

## STA 805: STATISTICAL INFERENCE AND BAYESIAN METHODS

Criteria of choice, and optimality consideration, in respect of point estimation, hypothesis tests and confidence intervals. Likelihood methods with special consideration of maximum likelihood estimates (m.l.e.) and likelihood ratio tests including multiparameter problems (and linearisation methods). Specific techniques will include: Hypothesis Testing:

Pure significance tests, simulation tests, Neyman Pearson Lemma, UMP test. Point Estimations: Efficiency, consistency, minimum variance bound estimators. Determination of m.l.e’s including linearisation and asymptotic properties, maximum likelihood ratio tests and large-sample equivalents, asymptotic optimality. Score tests. Jackknifing, bootstrapping. Prior distributions: Representation of prior information via a prior distribution, substantial information, vague priors and ignorance, empirical Bayes ideas. Normal Models: Theory for unknown), prior-posterior-predictive, normal regression model. Comparisons: Comparisons of classical, Bayesian, decision-theory approaches and conclusions via specific examples.