**Distribution of Courses: (B.Sc.) Statistics**

**100 Level**

FIRST SEMESTER | |||

Course Code | Course Title | Credits | Status |

STA 110 | Introduction to Statistics | 4 | Core |

MTH 110 | Algebra and Trigonometry | 3 | Core |

MTH 112 | Calculus | 3 | Core |

CSC 110 | Introduction to Computing | 3 | Core |

PHY 111 | Mechanics, Thermal Physics and Properties of Matter | 3 | Elective |

PHY109 | Practical Physics I | 2 | Elective |

GST 111 | Use of English | 2 | Core |

GST 112 | Philosophy and Logic | 2 | Core |

ECO111 | Principles of Economics | 3 | Elective |

Total Credits | 25 |

SECOND SEMESTER | |||

Course Code | Course Title | Credits | Status |

MTH 123 | Vectors and Coordinate Geometry | 3 | Core |

MTH 125 | Differential Equations and Dynamics | 3 | Core |

PHY 124 | Electromagnetism and Modern Physics | 4 | Elective |

GST 121 | Peace and Conflict Resolution | 2 | Core |

GST 122 | Nigerian Peoples and Culture | 2 | Core |

GST 123 | History and Philosophy of Science | 2 | Core |

ECO121 | Principles of Economics II | 3 | Elective |

Total Credits | 19 |

__Electives__: At least 12 credits of 100 – Level courses in the Faculties of Life and Physical Sciences and Departments of Economics and Business Administration.

**200 LEVEL**

FIRST SEMESTER | ||||

Course Code | Course Title | Credits | Status | |

STA 211 | Probability Distribution Theory I | 3 | Core | |

CSC 212 | Symbolic Programming in FORTRAN | 3 | Mandatory | |

MTH 230 | Linear Algebra | 3 | Core | |

MTH 218 | Mathematical Methods I | 3 | Core | |

MTH 212 | Real Analysis I | 3 | Mandatory | |

STA 214 | Operations Research I | 3 | Mandatory | |

STA 212 | Statistics for Agriculture & Behavioral | 3 | Elective | |

STA 213 | Introduction to Social and Economic Statistics | 3 | Elective | |

MTH 210 | Elementary Algebra and Analysis | 3 | Elective | |

Total Credits | 27 |

SECOND SEMESTER | |||

Course Code | Course Title | Credits | Status |

STA 221 | Statistical Inference I | 3 | Core |

STA 222 | Statistical Computing I | 3 | Core |

MTH 228 | Mathematical Methods II | 3 | Elective |

MTH 227 | Introduction to Numerical Analysis | 3 | Core |

CSC 220 | Introduction to Data Processing | 3 | Elective |

STA223 | Statistics for Physical Sciences & Engineering | 3 | Elective |

Total Credits | 18 |

**300 LEVEL**

FIRST SEMESTER | |||

Course Code | Course Title | Credits | Status |

STA 311 | Analysis of Variance and Regression Analysis I | 3 | Core |

STA 312 | Probability Distribution Theory II | 3 | Core |

STA 313 | Statistical Computing II | 3 | Core |

STA 314 | Operations Research II | 3 | Mandatory |

STA 331 | Sampling Theory and Survey Methodology | 3 | Mandatory |

MTH 324 | Mathematical Modelling | 3 | Elective |

CED 300 | Entrepreneurship Development | 2 | Mandatory |

Total Credits | 24 |

SECOND SEMESTER | |||

Course Code | Course Title | Credits | Status |

STA 324 | Biometric Methods I | 3 | Elective |

STA 321 | Statistical Inference II | 3 | Core |

STA 399 | Field Work/Industrial Training | 3 | Core |

STA 326 | Demography | 3 | Elective |

MTH 328 | Mathematical Methods III | 3 | Elective |

STA 325 | Econometric Methods | 3 | Elective |

Total Credits | 20 |

**400 LEVEL**

FIRST SEMESTER | ||||

Course Code | Course Title | Credits | Status | |

STA 431 | Non Parametric Statistics | 4 | Mandatory | |

STA 412 | Design and Analysis of Experiments | 4 | Mandatory | |

STA 454 | Biometric Theory II | 4 | Elective | |

STA 455 | Topics in Applied Statistics | 4 | Mandatory | |

STA 456 | Logical Backgrounds of Statistics and Decision Theory | 4 | Elective | |

STA 499 | Reading Course | 6 | Core | |

STA 411 | Probability Theory and Stochastic Processes | 4 | Mandatory | |

Total Credits | 30 |

SECOND SEMESTER | |||

Course Code | Course Title | Credits | Status |

STA 421 | Analysis of Variance and Regression Analysis II | 4 | Elective |

MTH 427 | Optimization Theory | 4 | Elective |

STA 432 | Bayesian Inference | 4 | Elective |

STA 449 | Statistical Inference III | 4 | Elective |

STA 469 | Linear Models | 4 | Elective |

STA 422 | Multivariate Analysis | 4 | Mandatory |

STA 441 | Time Series Analysis | 4 | Elective |

Total Credits | 28 |

**COURSE DESCRIPTION**

STA 110 – INTRODUCTION TO STATISTICS (4 CREDITS)

Introduction to Descriptive Statistics. Statistical data, sources, collection and presentation by tables and graphs, construction of Questionaires, Measures of location, partition, dispersion, skewness and kurtosis. Trimmed mean. Regression and Correlation: Least squares estimation of simple, Linear regression, interpretation of regression coefficient: use of regression. The product moment and rank correlation coefficients, their interpretation and use. Hypothesis testing. Elementary time series analysis. Introduction to Probability: Sample space and generation of statistical events from set-theory. Addition and Multiplication Law. Use of permutation and combination in evaluating probability. Probability sampling from tables of Random Numbers. Types and distribution of Random variables; the Binomial, Poisson, Hypergeometric, normal, Student’s t and chi-square distributions. Exploratory data analysis.

Remark: STA 110 is a combination of STA 111, STA 112 & part of STA 121 in BMAS.

STA 211 – PROBABILITY DISTRIBUTION THEORY I (3 CREDITS)

Distribution and frequency functions. Documents, cumulants and their generating functions. Some special univariate distribution. Laws of large numbers. Stochastic independence. Permutation and combination. Probability: Finite sample space, axioms of probability, simple theorems, concepts of probability, Simple theorems, concepts of probability, addition and multiplication rules, conditional probability and independence, tree diagrams, Bayes’ theorem combinatorial analysis. Expectations and moments of random variables. Chebyshev’s inequality. Probability distributions: random variables, means and variances, binomial, hypergeometeric, Poisson and normal distributions. Joint, marginal and conditional distributions. Limiting distributions. Moments and moment generating functions.

Remark: STA 211 is a combination of STA 211 & part of STA 312 in BMAS.

STA 212 – STATISTICS FOR AGRICULTURAL AND BIOLOGICAL SCIENCES (3 CREDITS)

Use of statistical Methods in biology and agriculture. Frequency distributions. Laws of probability. The binomial, Poisson and normal probability distributions estimation and tests of hypothesis. Experimental design variance and covariance, simple regression and correlation, contingency tables, some non parametric tests.

STA 213 – INTRODUCTION TO SOCIAL AND ECONOMIC STATISTICS (3 CREDITS)

Statistic systems. Nature, types, sources, methods of collection and problem of official statistic. Index numbers, theory, construction and problems. Socio-economic indicators: nature, types, uses and computation. Nature, sources, contents and problems of official statistic in selected sectors.

STA 221 – STATISTICAL INFERENCE I (3 CREDITS)

Revision of descriptive statistics; measures of location and dispersion, graphical representation of data as well as population and samples. The histogram: aesthetic histogram and density histogram. Population and samples. Random sampling distribution. Inference about means, proportions and standard deviations, large and small samples. The chi-square test of independence and goodness-of-fit. One way analysis of variance. Correlation and regression; tests of simple regression and correlation coefficients. Estimate and prediction in multiple regression. Introductory inference; meaning and existence of sampling distribution, sampling distribution of the mean and proportion in large samples, point and interval estimation of means and proportions, simple hypothesis testing.

Remark: STA 221 is a combination of part of STA 121 & STA 221 in BMAS.

STA 222 – STATISTICAL COMPUTING I (3 CREDITS)

Use of computers in statistical computing. Computations based on curve fitting, goodness – of – fit tests, estimation, hypothesis and contingency tables. Introduction to packages such as spreadsheets, MINITAB, SPSS, Eview, D – Base, etc.

STA 223 – STATISTICS FOR PHYSICAL SCIENCES AND ENGINEERING (3 CREDITS)

Measures of location and dispersion in simple and grouped data. Elements of probability and probability distributions: normal, binomial, Poisson, geometric, negative binomial, exponential distributions. Regression, correlation and analysis of variance, contingency table. Non – parametric inference.

STA 214 -Operations Research I (3 Credits)

Nature and scope of operations research. Model Building (including history, definitions) survey of common techniques, role of OR in industries, distraction and relationship with management: case studies. Basic OR techniques; LP: concept of simulation. Elements of Network analysis and dynamics programming. Inventory theory and applications. Sequencing and scheduling.

STA 331 – SAMPLING THEORY AND SURVEY METHODOLOGY (3 CREDITS)

Basic Sampling methods. Stratification. Use of auxiliary information. Multi-state sampling. Non-sampling errors. Estimation of population mean and stratified random sampling. Methods of social investigation: Planning survey, problems, design of surveys, errors and bias, methods of collection of data, design of forms and questionnaire, processing, analysis and interpretation. Nigeria’s experience in sampling surveys.

STA 311 – ANALYSIS OF VARIANCES AND REGRESSION ANALYSIS I (3 CREDITS)

Analysis of Variance: Analysis of simple, double and multiple classification of balanced data in crossed and nested arrangements. Analysis of two-ways, three ways contingency tables for tests of homogeneity, independence and inter actions, analysis involving incomplete tables, missing values, etc. Partial and multiple correlation. Regression Analysis: Multiple linear regression models, polynomial regression. Tests of independence and goodness – of – fit. Use of dummy variables. Non linearity in parameters requiring simple transformation. Orthogonal polynomial. Time series.

STA312 – PROBABILITY DISTRIBUTION THEORY II (3 CREDITS)

Distribution of quadratic forms. Fisher-Cochran theorem, multivariate normal distributions. Distribution of order statistics from continuous populations. Characteristic and moment generating functions. Uniqueness and inversion theorems. Limit theorems. Discrete and continuous probability distributions. Mathematical expectation and moments of random variable. Moment generating functions. The binomial, poisson, geometric, hypergeometric and negative binomial distributions. The normal, uniform, gamma and beta distribution. The central limit theorem (proof by m.g.f.). Functions of univariate random variable. Bivariate distributions. Bivariate moment generating functions of random variable. Bivariate moment generating functions. Bivariate normal distributions. Distribution associated with the normal, X2, t and F distribution. Independence. Sums of independent random variables. Allocation and matching problems.

Remark: STA 312 is a combination of part of STA 312 & STA 311 in BMAS.

STA 313 – STATISTICAL COMPUTING II (3 CREDITS)

Statistical computing using modern computer packages such as STAT, R, Gretl, SAS, GENSAT, S-PLUS and the use of statistical toolbox in Matlab, etc. Recoding and Variable Transformations. Analysis of statistical and numerical algorithms. Introduction to Monte Carlo methods.

**STA 321 – STATISTICAL INFERENCE II (3 CREDITS)Principles, criteria and methods of estimation; moment methods and maximum likelihood. Least squares and method of moments. Use of unbiasedness and minimum variance in selecting good estimators. Interval estimation derivation of point and interval estimators of means, proportions and standard deviations. Principles of hypothesis testing; type I and II errors. Power curve. Chi-square and F-tests. Likelihood ratio test. Use of non-parametric tests: the sign and median tests. Wilcoxon two sample rank test. Analysis of variance: two-way analysis. Sources and detection of process variation. Quality control; acceptance sampling, control charts, cumulative sum techniques. Control charts for attributes and variables and their properties. Cumulative sum charts and their properties. Continuous sampling plans.Remark: STA 321 is a combination of part of STA 321 & STA 341 in BMAS.**

STA 314-OPERATIONS RESEARCH (3 CREDITS)

Phase of operations research study: Classification of operations research models. Linear, dynamic and integer programming. Decision Theory. Inventory models. Critical path analysis and project controls.

STA 324 – BIOMETRIC THEORY I (3 CREDITS)

Introduction to population genetics. Statistical methods in Biology. Sampling and estimating biological populations. Design and analysis of biological experiments. Design and analysis of clinical trials. Bioassays: types and nature. Direct and indirect assays: parallel line assays, slope ratio assays. Use of Epi Info package.

STA 325 – ECONOMETRIC METHODS (3 CREDITS)

Nature of econometric. Econometric models: nature, types and characteristics. Econometric problems related to single equation models. Construction, estimation and tests. Models involving lagged variables. Simultaneous equation systems: structural form, reduced form, identification, estimation and test. Application of econometric models: demand analysis, production functions, consumption and investment function.

STA 326 – DEMOGRAPHY (3 CREDITS)

Types and sources of demographic data. Methods of collection of population censuses, sample surveys and vital registration. Evaluation of the quality of demographic data. Measures of fertility, mortality, nuptiality and migration. Standardization and decomposition. Life tables: construction and application. Framework for developing demographic information systems.

STA 399 – FIELD WORK/INDUSTRIAL TRAINING (2 CREDITS)

Computations based on field work and laboratory appraisal of statistical techniques such as survey methods and sampling theory and experimental design. Students will be assessed based on seminar presentation and assessment by a panel set up by the department.

STA 499 – READING COURSE [STUDENT PROJECT] (6 CREDITS)

The student undertakes a course of reading and Laboratory work under the supervision of a Lecturer. There will in general not be formal lectures. The student consults the supervisor as often as is necessary. At the end of the course, the student submits a written subsume of the topic and gives a talk before a Departmental evaluation board.

**STA 411 – PROBABILITY THEORY AND STOCHASTIC PROCESSES (4 CREDITS)Probability spaces, measures and distribution. Distribution of random variables as measurable functions. Product of measurable spaces. Weak convergence almost everywhere. Laws of large numbers. Proability generating functions. Convolutions and compound distributions. Branching processes. Random walks, Markov Chains, Poisson, birth, birth-and-death processes. Queueing theory.Remark: STA 411 is a combination of STA 411 & STA 414 in BMAS.**

STA412 – DESIGN AND ANALYSIS OF EXPERIMENTS(4 CREDITS)

Design and Analysis of experiments: replication and randomization, completely randomized blocks and Latin square designs. Split plot design and nested designs, unbalanced designs, incomplete block designs. Factorial experiments: 2k full factorial and fractional factorial designs. Confounding and aliases. Further analysis of treatment effects: orthogonal contrasts and multiple comparisons. Investigation of assumptions and theory of tests. Introduction to response surface methodology.

Remark: STA 412 is a combination of STA 323 & STA 423 in BMAS.

STA 413 – SAMPLING THEORY AND SURVEY METHODS II

(4 CREDITS)

Quality control acceptance sampling, control chart, cumulative sum techniques. Survey methodology planning of surveys, simple random, stratified, cluster and systematic scenes. Sampling for means, totals and proportions. Sample size allocation in stratification. Comparison of precisions. Ratio and Regression Estimation. Two Stage Sampling.

STA 429 – SAMPLING THEORY AND SURVEY METHODS II (4 CREDITS)

Quality control, acceptance sampling, control charts, cumulative sum techniques. Process capacity studies and control charts. Survey Methodology, Planning of surveys, simple random, stratified, cluster and systematic sampling. Sampling for means, totals and proportions. Sample size allocation in Stratification. Comparison of precisions, Ratio and Regression Estimation, two stage sampling.

Remark: STA 429 is a combination of STA 341 & STA 424 in BMAS.

STA 421 – ANALYSIS OF VARIANCE AND REGRESSION ANALYSIS II (4 CREDITS)

Analysis of variance: Analysis of variance involving unbalanced data. Multivariate analysis of variance. Analysis of multi-factor, multi-response of variance such as missing observations. Non-normality, heterogeneity of variance etc. Regression Analysis: Partial and conditional regression and correlation models. Tests of independence of regression, Multicollinearity and other problems associated with “Best Regression Models”.

STA 422 – MULTIVARIATE ANALYSIS (4 CREDITS)

Multivariate normal and related distributions. Inference about mean vectors, Hotellings r2 and Mahalanobis D2 statistics. Discrimination and classification. Tests of independence. Principal components and factor analysis. Canonical correlation analysis. Cluster analysis.

STA 431 – NON-PARAMETRIC STATISTICS (4 CREDITS)

Order statistics and their distributions. Kolmogorov type of test statistic. Common non-parametric test including runs, sign, rank order and rank correlation. Null distributions and their approximations. Efficiency properties, Estimates based on test statistics. Measure of association for bivariate samples and multiple classifications.

STA 432 – BAYESIAN INFERENCE (4 CREDITS)

Bayes’ Theorem. Posterior and prior distributions. One parameter cases in some standard continuous and discrete distributions. Point and interval estimation. Prediction. Prediction of future observation. Choice of priors: natural conjugate families of prior distribution, simple non-informative priors. Comparison of the means and variance of two normal and Poisson distributions. Linear regression. Tests of hypothesis.

STA 441 – TIME SERIES ANALYSIS (4 CREDITS)

Estimation and isolation of components of time series. Non-stationary and stationary processes: theoretical moments, auto-correlation and partial auto-correlation; sample moments: univariate. Time series model: identification and estimation – auto-regressive (AR), moving average (MA) and auto-regressive moving average (ARMA). Diagnostic checking of models, linear prediction and forecasting spectral (harmonic) analysis.

STA 449 – STATISTICAL INFERENCE III (4 CREDITS)

Sampling and sampling distributions. Methods of point estimation. Properties of estimators, Interval estimation Rao-Blackwell theorem. Gramer-Raobounds. Significance tests. Neyman-Pearson theory. Likelihood ratio tests. Nonparametric tests, derivation of the sign, median, Wilcoxon and Mann-Whitney tests for two samples. Bayesian inference.

STA 454 – BIOMETRIC THEORY II (4 CREDITS)

Stability models, simultaneous selections models. Path analysis. Discriminant analysis. Parallel line and slope ratio assays in completely randomized block and incomplete block designs. Logistic curve and logic transformations in relation to bio-assays.

*STA 455 – TOPICS IN APPLIED STATISTICS (4 CREDITS)

Current topics in applied statistics are treated. The scope include, but not limited to, the following aspects: actuarial statistics, environmental statistics, educational statistics, energy statistics, life tables, medical and health statistics, population projection techniques and psychometric methods.

Remark: STA 455 is a combination of STA 452, STA 454, STA 455, STA 456, STA 457, STA 458, STA 459 & STA 461 in BMAS.

STA 456 – LOGICAL BACKGROUNDS OF STATISTICS AND DECISION THEORY (4 CREDITS)

Empirical sources of knowledge-hypothesis, observation and experiment. Deductive sources of knowledge and scientific attitude. The concept of causation. Probability, a brief historical treatment to show conflicting definitions. Bayesian statistics and the notion in inverse probability. The place of statistical methods in science. Principles of decision making. Utility functions and their properties. Role of uncertainty. Bayes strategies. Problems of prior and posterior distributions: value of prior information minimax strategies. Statistical inference. Theory of games.

***STA 469 -LINEAR MODELS (4 CREDITS)Revision of simple linear regression. Matrix theory revision of result. Multivariate normal distribution, marginal and conditional distributions’ Linear functions of normal variables Quaratic form, Multiple regressions. Least squares estimation. Gauss-Markov theorem. Maximum likelihood (ML) estimation, distribution of function of ML estimators, confidence regions. Hypothesis testing. Prediction, Orthogonality and multicollinearity. Model selection. Variables, Restricted regression; analysis of variance model**.

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