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LIST OF COURSES FOR THE AWARD OF B.TECH STATISTICS The courses to be offered leading to the award of B. Tech. Statistics are as follows: 100 LEVEL UNIVERSITY COURSES HARMATTAN SEMESTER Course Code Course Title L T P Units BIO 101 General Biology I 2 1 0 3 BIO 103 Experimental Biology I 0 0 1 1 CHM 101 General Chemistry I 3 1 0 4 CHM 191 Experimental Chemistry I 0 0 1 1 PHY 101 General Physics I 3 1 0 4 PHY 103 Experimental Physics I 0 0 1 1 MTH 101 Elementary Mathematics I 4 1 0 5 GNS 101 Use of English I 2 0 0 2 FAA 101 Fundamental of Basic Drawing 2 0 0 2 LIB 101 Use of Library 0 0 0 0 TOTAL 16 4 3 23 Rain SEMESTER Course Code Course Title L T P Units BIO 102 General Biology II 2 1 0 3 BIO 104 Experimental Biology II 0 0 1 1 CHM 102 General Chemistry II 3 1 0 4 CHM 192 Experimental Chemistry II 0 0 1 1 PHY 102 General Physics II 3 1 0 4 PHY 104 Experimental Physics II 0 0 1 1 MTH 102 Elementary Mathematics II 4 1 0 5 GNS 102 Use of English II 2 0 0 2 GNS 110 History of Settlements 2 0 0 2 CSE 100 Introduction to Computer 1 0 0 0 Total 17 4 3 24 200 LEVEL harmattan SEMESTER courses Course Code Course Title L T P Units Remark STA 201 Probability I 3 1 0 4 C STA 203 Inference I 4 0 0 4 C STA 205 Laboratory for Inference I 0 0 2 2 C STA 211 Descriptive Statistics 2 1 1 4 C MTH 201 Mathematical Methods I 2 1 0 3 C MTH 203 Linear Algebra I 2 0 0 2 C MTH 207 Real Analysis I 2 1 0 3 C CSE 201 Basic Computer Programming 2 0 0 2 C TOTAL 16 5 3 24 200 LEVEL rain SEMESTER courses Course Code Course Title L T P Units Remark STA 204 Inference II 4 0 0 4 C STA 206 Laboratory for Inference II 0 0 2 2 C STA 208 Probability II 3 1 0 4 C STA 212 History of Statistics 2 0 0 2 C MTH 202 Elementary Differential Equation I 2 1 0 3 C MTH 206 Linear Algebra II 2 0 0 2 C CSE 202 Overview of Computer Sci. & Eng. 2 0 0 2 C GNS 202 Logic, Philosophy and Science 2 0 0 2 C TOTAL 16 3 2 21 300 LEVEL harmattan SEMESTER courses Course Code Course Title L T P Units Remark STA 301 Distribution Theory 2 0 0 2 C STA 305 Regression Analysis I 1 1 0 2 C STA 307 Sampling Theory & Survey Methods I 4 0 0 4 C STA 309 Lab/Field work for sampling 0 0 2 2 C MTH 301 Abstract Algebra I 2 1 0 3 C MTH 307 Set, Logic and Algebra 2 1 0 2 C CSE 301 Computer Programming 2 1 0 3 C GNS 209 Element of Administration 2 0 0 2 C TOTAL 15 4 2 21 300 LEVEL rain SEMESTER courses Course Code Course Title L T P Units Remark STA 302 Probability III 3 1 0 4 C STA 306 Statistical Quality Control 4 0 0 4 E STA 308 Lab/Field work for Quality Control 0 0 2 2 E STA 310 Operations Research I 4 0 0 4 E STA 312 Laboratory for Operations Research I 0 0 2 2 E STA 314 Analysis of Variance I 1 1 0 2 C MTH 306 Real Analysis II 2 1 0 3 C TOTAL 13 4 4 21 NOTE: (i) Student must register for at least 6 units of the elective courses. (ii) The theory and laboratory work of the electives must be done concurrently. (iii) Minimum total units a student can register for is 15. (iv) Total units of compulsory courses is 9. 400 LEVEL harmattan SEMESTER courses Course Code Course Title L T P Units Remark STA 403 Stochastic Processes 3 1 0 4 E STA 405 Time Series 3 1 0 4 E STA 407 Design and Analysis of Experiments 2 1 1 4 C STA 409 Computer programming & statistical Packages 1 1 2 4 C STA 411 Inference III 4 0 0 4 C STA 413 Laboratory for Inference III 0 0 2 2 C STA 415 Biometry 3 1 0 4 E MTH 407 Lebesque Measure and Integration 2 1 0 3 C TOTAL 18 7 4 29 NOTE: (i) Student must register for at least 4 units of the elective courses. (ii) Minimum total units a student must register for is 21. (iii) A student cannot register for more than a total unit of 24. (iv) Total units of compulsory courses is 17. 400 LEVEL rain SEMESTER courses Course Code Course Title L T P Units Remark STA 410 Industrial Training (SIWES) 0 0 3 3 C 500 LEVEL harmattan SEMESTER courses Course Code Course Title L T P Units Remark STA 501 Probability Distribution IV 3 1 0 4 E STA 503 Analysis of Variance II 1 1 0 2 C STA 505 Regression Analysis II 1 1 0 2 C STA 507 Demography 2 0 0 2 E STA 509 Laboratory and field work for Demography 0 0 2 2 E STA 511 Multivariate Statistical Analysis 3 1 0 4 E STA 513 Sampling Theory & Survey Method II 3 1 0 4 E STA 599 Project 0 0 3 3 C TOTAL 12 6 5 23 NOTE: (i) Student must register for at least 8 units of the elective courses. (ii) Minimum total units a student must register for is 15. (iii) Any student willing to register for more than 24 units but not more than 28 units must request for permission to do so from the University through the Department and Faculty. (iv) Total units of compulsory courses is 7. 500 LEVEL rain SEMESTER courses Course Code Course Title L T P Units Remark STA 502 Decision Theory 3 1 0 4 C STA 504 Non Parametric Methods 3 1 0 4 C STA 506 Operations Research II 4 0 0 4 E STA 508 Laboratory for Operations Research II 0 0 2 2 E STA 512 Psychometry 3 1 0 4 E STA 599 Project 0 0 3 3 C MTH 508 Measure Theory 2 1 0 3 E TOTAL NOTE: (i) 14 5 5 24 Student must register for at least 6 units of the elective courses. (ii) Any Student who registers for STA 506 must also register for STA 508. (iii) Minimum total units a student must register for is 17. (iv) Any student willing to register for more than 24 units but not more than 28 units must request for permission to do so from the University through the Department and Faculty. (v) Total units of compulsory courses is 11. COURSE CONTENTS 200 LEVEL harmattan SEMESTER courses STA 201 PROBABILITY 1;3-1-0 (4 UNITS) Generation of statistical events from set-theory and combinatorial methods. Elementary principle of probability. Types and distribution of random variable the binomial, Poison, hyper geometric, normal distribution. Expectations and moments of random variables. Probability sampling from table of random numbers, Selected applications. STA 203 INFERENCE 1 4-0-0 (4 UNITS) Statistical data their sources, collection and primary analysis by tables and graphs. Time series, Demographic measures and index numbers. Inference: estimation and tests of hypotheses. Regression and correlation. STA 205 LABORATORY FOR INFERENCE 1 0-0-2 (2 UNITS) Presentation and analysis of data: Curve fitting and goodness – of fit tests. Construction of questionnaires and simple index numbers. Use of random numbers and statistical tables. STA 207 STATISTICS PHYSICAL SCIENCES AND ENGINEERING 3-1-0 (4 UNITS) Measures of location and dispersion is simple and grouped data. Elements of probability and probability distributions. Estimations and tests of hypotheses concerning the parameters of distributions. Regression, correlation and analysis of variance. Contingency table. Non-parametric inference. STA 211 DISCRIPTIVE STATISTICS: 2-1-1 (4 UNITS) Basic Statistical Concepts. Introduction, Quantitative and Qualitative characteristics Sampling and nonsampling errors. Inductive inference from sample. Different methods of data collection, Classification – presentation and interpretation of data. Concepts and measure of location and dispersion Skewness and Kurtosis. Moments, Simple Regression and correlation. 200 LEVEL rain SEMESTER courses STA 204 INFERENCE II 4-0-0 (4 UNITS) Hypothesis Testing: Use of Neyman – pear fundamental Lemma, the power of a test. Point and internal estimation (Testing and estimation of large sample situations) binomial, Poisson, normal contingency tables, Goodness of fit tests. STA 206 LABORATORY FOR INFERENCE II: 0-0-2 (2 UNITS) Computations base on curve fittings, goodness of fit tests, estimation. Test of hypotheses and contingency tables. STA 208 PROBAILITY II: 3-1-0 (4 UNITS) Combinatoral analysis. Probability models for the study of random phenomenon if finite sample spaces Probability distributions of discrete and continuous random variables. Expectations and moments generating functions. Chebyshev inequality. Bi-variate marginal and conditional distributions and moments Convolution of two distributions and moments Convolution of two distributions, the central limit theorem and its uses. STA 210 STATISTICS FOR BIOLOGICAL AND AGRICULTURAL SCIENCES: 3-1-0 (4 UNITS) Use of statistical methods in Biology and Agriculture. Frequency distribution of Probability. The Binomial, Poison and Normal Probability Distribution. Estimation and test of hypothesis, Design of simple and Agricultural and Biological experiments. Analysis of variance and convariance. Simple Linear Regression and Correlation. Contingency Table. Some Non-parametric tests. STA 212 HISTORY OF STATISTICS: 2-0-0 ( 2UNITS) History of Statistics with emphasis on developments of various areas of the subject in 20th Century. 300 LEVEL harmattan SEMESTER courses STA 301 DISTRIBUTION THEORY: 1-1-0 (2 UNITS) The Gamma, Exponential, chi-square, 2type of beta, Normal, student-t F and bivariate Normal distributions. Distribution of functions random variables using cumulative distribution function, moment generating function and transformation techniques. probability integral transformation. Order statistics and their functions. STA 305 REGRESTION ANALYSIS I: 1-1-0 (2 UNITS) Pre-requisite-m STA 204 and STA 206 Multiple linear regression models polynomial regression. Test of independence and goodness - of - fit. Use of dummy variables. Non – linearity in parameter requiring simple transformation. STA 307 SAMPLING THEORY AND SURVEY METHODS I: 4-0-0 (4 UNITS) Pre-requisite – STA 204 Basic sampling methods: Simple random sampling, Stratification, Cluster. Use of auxiliary information. Non – sampling errors. Estimation of population mean and total in simple and in stratified random sampling. Methods of social investigation. Planning surveys, problems, design of surveys, errors and bias, methods of collection, of data, processing, analysis and interpretation. Nigeria’s experience in sampling surveys. STA 309 LABORATORY AND FIELD WORK FOR SAMPLING: 0-0-2 (2 UNITS) Field and laboratory appraisal of some of the techniques and problems in sample surveys. 300 LEVEL rain SEMESTER courses STA 302 PROBABILITY DISTRIBUTION III: 3-1-0 (4 UNITS) Pre-requisite – STA 208 Brief revision of basic probability concepts. Probability generating functions. Univariate and bivariate moment generating functions, Univariate characteristic functions. Inversion formula. Various modes of convergence. Laws of large numbers and central limit theorem using characteristics functions. Random walk and Markov chains. Introduction to Poisson process. STA 306 STATISTICAL QUALITY CONTROL: 4-0-0 (4 UNITS) Pre-requisite – STA 204 Process control: Use of control charts to achieve process stability. Tolerance limits as a function of component variability. Product control: Design of simple, double, multiple, and sequential sampling plans. Comparison of different sampling plans. Cumulative sum charts, feedback theory for controlling continuous process. STA 308 LABORATORY AND FIELD WORK FOR STATISTICAL QUALITY CONTROL: 0-0-2 (2 UNITS) Practical construction of control charts. Computations involving tolerance limits. Sample, multiple and sequential plans. Design and analysis of various rectification schemes. STA 310 OPERATIONS RESEARCH I: 4-0-0 (4 UNITS) Classical methods of optimization: Maxima and minima, Language’s multipliers. Linear programming: Convex sets and functions, simplex and revised simplex methods duality theory, applications. Game theory: two persons, zero- sum games, saddle point, dominance, strategies. STA 312 LABORATORY FOR OPERATIONS RESEARCH I: 0-0-2 (2 UNITS) Exercise on problem formulation involving linear programming applications. Computation using simple, revised simplex algorithms to solve non-trivial linear programming problems. use of linear programming computer package. STA 314 ANALYSIS OF VARIANCE I: 1-1-2 (2 UNITS) Pre- requisite - STA208 Analysis of simple, double and multiple classifications of balanced data in crossed and nested arrangements. Analysis of two-ways, three ways contingency tables for test of homogeneity, independence and interactions. Analysis involving incomplete tables missing values. 400 LEVEL harmattan SEMESTER courses STA 403 STOCHASTIC PROCESES: 3-1-0 (4 UNITS) Pre- requisite - STA 302. Random walk: simple and general random walk with absorbing and reflecting barriers. Markovian processes with finite chain. Limit theorems. poison, branching, birth and dearth processes. Queing processes: M/ M/ I, M/ M/ S, M/ G/ I queues and their waiting time distributions. Relevant applications. STA 405 TIME SERIES: 3-1-0 (4 UNITS) Pre-requisite – STA 305 Components of time series. Measurement of trend, seasonal index, the cyclical component and random fluctuations. Series correlation, correlogram. Stationary time series. Estimation of means and their covariance function. Model identification. linear prediction in time series, autoregressive series. STA 407: DESIGN AND ANALYSIS OF EXPERIMENTS 2-1-1 (4 UNITS) Pre-requisite – STA 301 Application of statistical methods to the efficient design of experiments. One factor and multi-factor experiments in randomized block, incomplete blocks, Latin squares, split-plots, etc. 2n factorial experiments with confounding and fractional replications. Problems in experimentation; Missing values, heterogeneous data. STA 409 COMPUTER PROGRAMMING AND STATISTICAL PACKAGES: 1-1-2 (4 UNITS) Writing of statistical programmes using some of these languages: BASIC, FORTRAN, PASCAL, C+, C++, etc. analyzing data using some of these statistical packages: SPSS, SAS, STATA, GENSTAT, MINITAB, etc. STA 411 INFERENCE III: 4-0-0 (4 UNITS) Pre-requisite - STA 204 Statistic: Sufficiency, completeness point Estimation: Methods of moments, of least of squared errors, of maximum likelihood. Properties of Point Estimation: Unbiasedness, Fisher Information, Gramer – Rao Inequality, Efficiency, asymptotic efficiency, Uniformly Minimum Variance Unbiased Estimator, Consistency, Best Asymptotic Normality. Confidence Intervals and Regions: General method of finding a confidence bound, large sample confidence intervals. Gauss – Markov and Fisher – Cochran theorems. Tests of hypotheses: Simple vs Simpe – Best Test, Most Powerful Test – use of Neyman – Pearson Fundamental Lemma. STA 413 LABORATORY FOR INFERENCE III: 0-0-2 (2 UNITS) Computations involving point and interval estimation. Tests of hypothesis. Analysis of variance, goodness – of – fit tests and contingency tables. STA 415 BIOMETRY: 3-1-0 (4 UNITS) Purpose, history and structure of biological assays. International standards. Statistical Science and biological assays. Terminology and notations. Types of biological assays Nature of direct assays. Applications to strophanthus. Precision of estimates 400 LEVEL rain SEMESTER courses Industrial Attachment Period 500 LEVEL HARMATTAN SEMESTER courses STA 501 PROBABILITY DISTRIBUTION IV: 3-1-0 (4 UNITS) Pre-requisite – STA 302 Probability spaces, measures and distributions. Distributions of random variables as measurable functions. Product spaces, product of measurable spaces, product probabilities. Independence of and expectation of random variables. Convergence of random variables: Weak convergence, convergence almost everywhere, convergence in mean. Central limit theorem laws of large number. Characteristics function. STA 503 ANALYSIS OF VARIANCE II: 1-1-0 (2 UNITS) Pre- requisite – STA 314 Analysis of variance involving unbalanced data. Multi- variate analysis of variance Analysis of nultifactor, multi-response of variance such as missing observation Non-normality, heterogeneity of variance, etc. STA 505 REGRESSION ANALYSIS II: 1-1-0 (2 UNITS) Pre-requisite – STA 305 Partial and conditional expectation of Y green Xn correlation models, partial and correlation models. Canonical correlation. Test of independence of regression coefficients. Multicolinearity and other problems associated with ‘Best Regression Models’ STA 507 DEMOGRAPHY: 2-0-0 (2 UNITS) Demographic data: Sources, assessment of and use in construction of life tables. Definition of basic concepts. Estimation of population parameters from defective data. Stable and quasi – stable population, population projections. STA 509 LABORATORY AND FIELD WORK FOR DEMOGRAPHY: 0-0-2 (2 UNITS) Exercises on assessment of and use in construction of life tables; estimation of population parameters from defective data, stable and quasi – stable population; and population projections. STA 511 MULTIVARIATE STATISTICAL ANALYSIS: 3-1-0 (4 UNITS) Multivariate Normal distribution and associated marginal and conditional distributions. Estimation of mean vector and variance – covariance matrix. Hotelling T2 and mahalanobi’s D2. Test of hypotheses. Discriminant Function. Classification Principal Components and Factor Analysis. STA 513 SAMPLING THEORY AND SURVEY METHODS II: 3-1-0 (4 UNITS) Pre- requisite – STA 307 Single and multi – stage cluster sampling. Equal and unequal clusters. Double sampling Further use of auxiliary information. Multivariate ratio estimation. Unequal probability sampling with or without replacement. Ordered or unordered estimators. 500 LEVEL rain SEMESTER courses STA 502 DECISION THEORY: 3-1-0 ( 4 UNITS) Pure or Mathematical Game ( , A, L). Admissibility of action with respect to the action space a and the loss function L: ( X A) . Minimax and Bayes action. Statistical Game ( , D, R) : Admissibility of a decision ruled with respect to the decision space D and the risk function R ( , d) = E., L ( ,d(X)). Minimax and Bayes decision rule. Estimation Conjugate prior and bayes estimator. Hypothesis Testing: Best test MP test and Bayes test of simple hypothesis vs. simple hypothesis. UMP test of one sided alternative. STA 504 NON-PARAMETRIC METHODS: 3-1-0 (4 UNITS) Pre- requisite – STA 302 and STA 411 Order statistics and their distribution. Kolmogorov type of test statistic. Common non-parametric test including runs, sign rank order and rand correlation. Null distributions and their approximations. Efficiency properties. Estimates based on test statistics. STA 506 OPERATIONS RESEARCH II: 4-0-0 ( 4 UNITS) Integer programming: Problem formulation and methods of solution. Non-linear programming: Search methods, Newton’s Raphson method, Frit – John optimality conditions and Lagrangian multipliers. Network analysis. Path methods including Bellman’s equations, cyclic and network with positive path. Inventory theory and applications. Dynamic programming routine of problems, resource allocation and equipment replacement. STA 508 LABORATORY FOR OPERATIONS RESEARCH II: 0-0-0 (2 UNITS) Exercises on problem formulation involving integer linear programming. Computations using Branch and Bound algorithm. Exercises on non – linear programming, network analysis (including project management, transportation and assignment problem). Dynamic programming problems. Use of various computer packages to solve problems. STA 512 PSYCHOMETRY: 3-1-0 (4 UNITS) Pre-requisite – STA 302 and STA 411 The foundations of mental measurement theory. Measurement in psychology and education. The classical test theory model: fixed length, variable length. Some estimates of parameters of the classical model. Other weak true – score models, parallel measurements. Types of reliability co-efficients and their estimation. Some test theory for equivalent measurements. Items, sampling in test theory and in research design. STA 599 PROJECT: (6 UNITS) Individual work on a selected topic illustrating application of some of the theories and techniques covered in the course. SPILL – OVER STUDENTS Any student that could not graduate having used the normal five years or four years or any number of years expected to be used (depending on the mode of entry) in the programmes is a spill over student. NOTE: Any Spill – over Student who wishes to register for courses with total units less than 12 or more than 24 but not 28 must request for permission to do so from the University through the department and faculty at the beginning of the semester. MINIMUM Requirements FOR GRADUATION Apart from the fact that a student must be found worthy, both in character and learning, of the award of B. Tech Statistics degree, he / she also must have: (i) passed all the 100 level University courses. (ii) passed all the 113 units of compulsory courses. (iii) passed all the 24 units of elective courses.