Motto: 'Critical Thoughts for Critical Minds'

# BSc. Statistics

**Entry Requirements**

The Department admits students into 100 level as well as 200 level for the B.Sc (Hons.) Statistics based on
their qualifications. In rare cases they may be admitted into upper levels.

**I. For 100 level: **
Candidates must satisfy the general University and Faculty of Science requirements of five O’Level credits
which must include: Mathematics, English, Physics and any other two relevant science subjects at Senior
Secondary School Certificate level or examination in at most two sittings.

**II. For 200 level: **
Candidates must in addition to (I) above have an Advanced level (A ‘Level) or its equivalence in Statistics and
any other science subject.

**Duration of the programme**

The duration of B.Sc. (Hons.) Statistics programme is four years for candidates admitted into 100 level and three years
for those admitted into 200 level. There are two semesters of formal University Studies in each academic session
except at 300level where students are required to undergo Students’ Industrial Work Experience Scheme (SIWES)
programme for 6 months. At the end of the programme, each student is required to write, present and defend a
report on what he/she learned in the industry. At 400 level, students undertake a one year project in any field
of interest.

**Graduation Requirements**

For a student to graduate, he/she must pass all his/her core courses, earn at least 120 credit units (i.e. TECU ≥ 120)
and have a Cumulative Grade Point Average of at least 1.50 (i.e. CGPA ≥ 1.50)

**BSc. Statistics Courses **

**Copyright © 2017 - All Rights Reserved - Department of Statistics (ABU Zaria)**

**MATH101 – Sets and Number System (2 Credit Units):**

**Prerequisite – O/Level Mathematics**
Sets: Definition of a set, finite and infinite sets, equality of sets, subsets, union, intersection, universal set, complements,
empty set, Venn diagram. Symmetric difference, power sets and De-Morgan theorems. Inclusion-Exclusion principle. Elements of
relations and functions.

Some Properties of number systems: Natural numbers, integers, rationals, irrationals and reals. Order relations in the set of
real numbers. Open and closed intervals on the number line.

Complex Numbers: Definition of a complex number, addition, multiplication and division. Geometric interpretation modulus and
conjugation. Polar representation, De- Moivre’s theorem, nth roots of a complex number, nth roots of unity.

**Text Books:**

1. Mathematics for Fresh Undergraduates Vol. I, D. Singh, A. Mohammed, A.M. Ibrahim and I.A. Fulatan ABU press (2013)

2. Set Theory and Related Topics, S. Lipschutz, (Schaum’s Outline Series), McGraw-Hill (1964).

**MATH103 – Trigonometry and Coordinate Geometry (2 Credit Units) :**

**Prerequisite – O/Level Mathematics**
Circular Measures: Trigonometric ratios of angles of any magnitude, inverse trigonometric functions.
Addition formulae: Sin (A+B), cos(A+B), tan(A+B) and their proofs. Multiple and half angles, solutions of simple trigonometric
equations. Factor formulae. Solution of triangles, heights and distances (including three-dimensional problems)

Plane Polar Coordinates: Relation between polar and Cartesian coordinates, plotting and sketching of simple curves whose polar
equations are known.

Coordinate Geometry of lines and Circles: Pair of straight lines and system of circles. (Emphasis on concepts rather than formulae).

**Text books:**

1. Mathematics for Fresh Undergraduates Vol. II, B.K. Jha, A.O. Ajibade, M.I. Yakubu and A.T. Imam, ABU press (2013)

2. Pure Mathematics Books I & II, J.K. Backhouse et al, Longman (1980)

2. Calculus and Analytical Geometry, G.B. Thomas and R.L.Finney, Addison- Wesley, (1979).

3. Theory and Problems of Trigonometry, Frank Ayres, (Schaum’s Outline Series). (1954).

**MATH105 – Differential and Integral Calculus (2 Credit Units) :**

**Prerequisite – O/Level Mathematics**
Functions of a real variable: Odd, even, periodic functions and their symmetries, graphs, limits and continuity
(Intuitive treatment only)

Differentiation: First principle, techniques of differentiation in general. Higher derivatives.
Integration: Integration as the inverse of differentiation, techniques of integration in general, definite integral (Evaluation only).

**Text books:**

1. Mathematics for Fresh Undergraduates Vol. III, J. Singh, H.M. Jibril, A.J. Alkali, Y.M. Baraya and A. Umar, ABU press (2013)

2. Pure Mathematics Books I & II, J.K. Backhouse, et al Longman (1980).

3. Calculus and Analytic Geometry, G.B. Thomas and R. L. Finney, Addison –Wesley (1979).

**COSC101 - Introduction to Computing:**

**Prerequisite: O/Level Mathematics**
Introduction to computer systems. Components of computer systems and their functons. Windows operating systems and its utilities.
Hands-on explosure to Office application software (MS Office or Open Office): Word processing, spreadsheets, presentations,
graphics and databases. Introduction to and use of Internet tools and technologies.

Click here to download course material

**Suggested Lab work :**

Lecturers should develop laboratory exercises and assignments targeted at providing hands-on practical experience on all topics in
the syllabus. The exercises should cover the typical tasks that students do with computers throughout their studies.

**Textbooks:**

1. Fundamentals of information technology, S.B. Junaidu, A.F. Donfack-kana and A. Salisu, ABU press (2013)

2. Practical Computer Literacy, J.J. Parsons and D. Oja, Thompson Learning, (2005)

3. Curt Simmons, How to Do Everything with Windows XP, 2nd Edition McGraw-Hill/Osborne, 2003, ISBN 0-07-223080-0

4. Introduction to Computers, 5th Edition, Peter Norton’s, McGraw-Hill/Glencoe, 2003, ISBN 0-07-826421-9

**STAT102 - Introductory Statistics II (2 Credit Units) :**

**Prerequisite – O/Level Mathematics. **
Random experiment, Sample space, event space, definitions of probability, conditional probability, addition and multiplication
theorems, definition of random variable (discrete and continuous), mathematical expectations of a random variable,
addition and multiplication theorems of expectation, definition of moment, relationship between raw moments and central moments,
the bi-variate frequency distribution, fitting of curves by method of least squares, concepts of correlation and regression and
their coefficients, the rank correlation coefficient.

**Text Books:**

1. Statistics for Fresh Undergraduates, Yahaya A. and Nnamani C.N., ABU press (2013), Zaria.

2. Mathematical Statistics, Ray, M., Sharma, H.S. and Choudhary, S., Ram Prakash and Sons Agra - 3, India.

3. Fundamentals of Mathematical Statistics, Gupta S.C. and Kapoor, V.K., Sultan Chand and Sons, New Delhi, India.

**MATH102 – Algebra (2 Credit Units) :**

**Prerequisite – O/Level Mathematics**
Quadratic and other polynomial functions: Elementary properties of quadratic expressions, roots of quadratic equations,
application to symmetric functions, polynomial functions of third and fourth degrees, remainder theorem, location of roots.

Permutation and combination: Notion of Factorials, nPr, nCr, and simple applications, mathematical induction principle and applications.

Binomial Theorem: Expansion of all rational index, interval of convergence, approximations and errors.

**Text books:**

1. Mathematics for Fresh Undergraduates Vol. I, D. Singh, A. Mohammed, A.M. Ibrahim and I.A. Fulatan ABU press (2013)

2. Pure Mathematics Book I and II, J.K. Backhouse, et al, Longman (1980)

**MATH104 – Conic Sections and Application of Calculus
(2 Credit Units) :**

**Prerequisite – O/Level Mathematics. **
Conics: Properties of parabola, ellipse, hyperbola, rectangular hyperbola, their Cartesian and parametric equations,
problems involving elimination of parameters, tangents and normals.
Rate of Change: Velocity, acceleration and other rates.

Curve Sketching: Asymptotes, maxima and minima. Small increments, approximations and errors. Newton’s approximation,
simple application of integration to areas and volumes. Differential equations: First order differential equations only.

**Text books:**

1. Mathematics for Fresh Undergraduates Vol. II, B.K. Jha, A.O. Ajibade, M.I. Yakubu and A.T. Imam, ABU press (2013)

2. Mathematics for Fresh Undergraduates Vol. III, J. Singh, H.M. Jibril, A.J. Alkali, Y.M. Baraya and A. Umar, ABU press (2013)

3. Pure Mathematics Books I & II , J.K. Backhouse, et al, Longman (1980)

4. Calculus and Analytic Geometry, G.B. Thomas and R.L.Finney, Addison-Wesley (1979).

**MATH106 – Vectors and Dynamics (2 Credit Units) :**

**Prerequisite – O/Level Mathematics**
Vectors: Geometric representation of vectors in 1-3 dimensions, components, direction cosines. Addition, scalar multiplication,
linear independence and dependence of vectors. Scalar and vector products of vectors. Differentiation and integration of
vectors w.r.t a scalar variable.
Dynamics: Kinematics of a particle. Components of velocity and acceleration of a particle moving in a plane. Force, momentum,
laws of motion under gravity, projectiles, restricted vertical motion, elastic strings, simple pendulum, impulse.
Impact of two smooth spheres, and of a restricted sphere and a smooth sphere.

**Text books:**

1. Mathematics for Fresh Undergraduates Vol. III, J. Singh, H.M. Jibril, A.J. Alkali, Y.M. Baraya and A. Umar, ABU press (2013)

2. Textbook of Dynamics, F. Charlton, Ellis Horwood, 1977.

3. Vector Analysis, Murray R. Spiegel, Schaum’s Outline Series (1974)

**STAT201 – Discrete Probability Distributions (3 Credit Units) :**

**Prerequisite – STAT102.**
Brief revision of various definitions of probability. Bayes’ theorem, concepts of probability function, probability density function,
cumulative probability density function and moment generating function. Univariate discrete probability distributions such as Bernoulli
distribution, Binomial and Poisson distribution, type I and type II geometric distributions, negative binomial distribution,
hypergeometric distribution, various properties of all these distributions, fitting of binomial, Poisson and geometric distributions.

**Text Books:**

1. Statistics for Fresh Undergraduates, Yahaya A. and Nnamani C.N., ABU press (2013), Zaria.

2. Introduction to the theory of Statistics, Mood, A.M., Graybill, F.A. and Boes, D.C. Mc-Graw-Hill, New York, USA.

3. Fundamentals of Mathematical Statistics, Gupta S.C. and Kapoor, V.K., Sultan Chand and Sons, New Delhi, India.

**MATH201 – Mathematical Methods - I (3 Credit Units) :**

**Prerequisite – MATH105 or equivalence**
Applications of Calculus: Revision of different techniques of differentiation, successive differentiation, Leibniz’s theorem,
Taylor’s and Maclaurin’s series. Tangents and normals to plane curves, curvature, Definite integrals. Methods of integration,
reduction formulae, lengths of arc of a plane curve. Area enclosed by a plane curve.

Differential Equations: Concept of differential equations. First order ordinary differential equations of the forms:
variable separable, homogeneous, exact and linear. Second order ordinary linear differential equations with constant coefficients,
auxiliary equation, and cases of auxiliary equations having distinct, equal, and complex roots, complementary functions and
particular integrals in connection with non-homogeneous equations. Uses of the operator D = d/dx and the method of undetermined
coefficients for calculating particular integrals. Differential equations of Euler’s type of second order. Solutions of systems
of two linear differential equations. Second order Ordinary Linear Differential Equations with variable coefficients; reduction
of order, variation of parameters.

Partial Differentiation: Real valued functions of two and three variables. Partial derivatives, chain rule, Jacobian.
Extrema, Lagrange’s multipliers, increments, differentials and linear approximations.

**Text books :**

1. Mathematical Methods, J. Heading, University Press, (1963).

2. Advanced Engineering Mathematics, E. Kreyszig, Wiley, (1987).

**MATH203 – Real Analysis I (3 Credit Units) :**

**Prerequisite – MATH105 or equivalence**
Preliminaries: Properties of real numbers, algebraic and topological properties, identity theorem, density theorem for Q and R.
Ordering and properties.

Boundedness: Boundedness and related simple results.

Relations and Functions: Cartesian products of sets.

Relations: equivalence relations, equivalence classes.

Functions: injective, surjective, bijective, inverse, composition of functions, monotone functions, graph of functions,
algebraic operations on functions.

Sequences and series of Real Numbers: Sequences of real numbers, subsequences, bounded and unbounded sequences.

Limit of a sequence; limit superior and limit inferior, improper limits. Algebraic operations on sequences and their limits;
Monotone sequences and properties. Cauchy sequences and related results.

Series of real numbers: partial sums, convergence, absolute and conditional convergences. Convergence tests:
comparison, ratio, Ra’abe, De-Morgan and Betrand, logarithmic, Cauchy root tests. Cauchy condition for the convergence of series,
rearrangement of series.

**Text Books:**

1. Introduction to Real Analysis, A. Olubumo, Heinemann (1979).

2. Real Analysis (An introduction) White A.J, Addison – Wesley, (1968)

**MATH207 – Linear Algebra I (3 Credit Units) :**

**Prerequisite – MATH102 or equivalence**
Matrices: Definition, types of matrices, algebra of matrices, matrix as a sum of symmetric and skew symmetric matrices.
Elementary operations of matrices and echelon form, equivalent matrices. Inverse of a matrix.

Systems of linear equations and matrices: Systems of m linear equations in n unknowns and their solutions.
Gaussian elimination by pivot method and matrix representation. Solution of the system using Gaussian elimination andGauss-Jordan reduction.

Determinants: Definition, evaluation of determinants. Cofactor expansion, inverse of a non-singular matrix.
Solution of systems of linear equations using Cramer’s rule.

**Text books:**

1. Linear Algebra, S. lipscutz (Schaum’s Outline Series) Mc Graw-Hill (1987)

2. Linear Algebra and Matrix Theory, E.D. Nerring, John Wiley, (1967).

**MATH209 – Numerical Analysis I (3 Credit Units) :**

**Prerequisite – MATH105**
Accuracy in numerical calculations: errors and their sources, error accumulation in different operations.

Finite differences: difference operators and difference table.

Evaluation of functions: using series approximation, solution of polynomial, algebraic and transcendental equations, curve fitting.

Interpolation: Newton’s difference formulae, central difference formulae, Lagrange’s formula. Numerical differentiation.
Numerical Integration

**Text books:**

1. Introduction to Numerical Analysis, Carl-Eric Froberg, Addison-Wesley publication, (1981).

2. Theory and Problems of Numerical Analysis, Francis Scheid, Schaum’s Series (1968).

3. Numerical Analysis: An Introduction, S.A. Bhatti, Mathematics Departmental Library, (Lecture Notes, 1980’s).

4. Calculus of Finite differences and Numerical Analysis, P.P. Gupta & G.S. Malik.

**STAT202 - Continuous Probability Distributions and Distribution Techniques (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
Univariate continuous probability distributions such as Normal, Uniform, exponential, type I and type II beta and gamma distributions,
various properties of these distributions, fitting of normal distribution. Concept of Bi-variate probability distribution, joint,
marginal, conditional probability distribution, covariance and correlation of bi-variate r.v. sampling distribution and standard
errors of statistics, distribution of functions of random variables using the techniques such as cumulative distribution function
technique, moment generating function technique and transformation technique.

**Text Books:**

1. Introduction to the theory of Statistics, Mood, A.M., Graybill, F.A. and Boes, D.C. Mc-Graw-Hill, New York, USA.

2. Fundamentals of Mathematical Statistics, Gupta S.C. and Kapoor, V.K., Sultan Chand and Sons, New Delhi, India.

**STAT204 – Biometry – I (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
Purpose, history and structure of biological assays. International standards. Statistical science and biological assays.
Types of biological assays. Nature of direct assays. The dose-response curves, parallel line assays, potency ratio and calibration curves.

**Text Books:**

1. Biometry 3rd Edition, R. R. Sokal & F. James Rohlf. W. H. Freeman (1994)

2. Statistical Methods in Biological Assays, 3rd edition, Finney, D.J., Charles Griffith, London

**MATH204 – Real Analysis - II (3 Credit Units) :**

**Prerequisites – MATH105 or equivalent **
Real Functions of one Variable: Limits of functions. Improper limits (limits at + and - Algebraic operations on limits of functions.
Continuity of functions on sets and related results. Uniform continuity.

Derivatives: derivative of functions derivative of composition of functions. Higher order derivatives.
Algebraic operations on derivatives of functions. Differentiability and some related results.
Rolle’s and Mean value theorems, Taylor’s formula, L’Hospital’s rule, local and global extrema,
saddle points, monotonicity, geometrical interpretations.

Riemann Integration: Partition of an interval, refinement, Riemann sums, Riemann integrals, uniqueness of Riemann integral,
Darboux integral of a real valued function, relation between Riemann and Darboux integrals.

**Text books :**

1. A first course in Real Analysis, Protter , M.H. and Morrey, C.B, Springer-Verlag, (1977).

2. Introduction to real Analysis, A. Olubumo, Heinemann (1979).

**MATH208 – Linear Algebra II (3 Credit Units) :**

**Prerequisite – MATH102**
Vector Spaces: Review of basic definitions and examples of vector spaces. Subspaces, linear dependence and independence.
Bases, dimension of a vector space. Homomorphism and quotient space. Direct sum, Dual spaces.

Linear Mappings and Matrices: General linear transformation of n-dimensional into m-dimensional space, matrix representation
of a linear map, similar matrices and change of basis. Eigenvalues and eigenvectors. Characteristic polynomial and characteristic
equation. Caley-Hamilton theorem. Orthogonal diagonalisation Canonical Forms: Primary decomposition theorem, Triangular Jordan and
Rational forms for linear operator (square matrices). Quadratic and bilinear forms.

**Text books:**

1. Linear Algebra, S. lipschutz (Schaum’s Outline Series) Mc Graw-Hill (1987)

2. Linear Algebra and Matrix Theory, E.D. Nerring, John Wiley, (1967).

**COSC202: Fortran and Structured Programming:**

**Prerequisite – COSC101 or Equivalence **
Structuered programming elements, structured design principle, abstraction, modularity, stepwise refinement, structured design techniques,
Teaching of structured programming language, FORTRAN: Characters, constant and variables, Arithmetic assignment statement.
FORTRAN standard functions. READ and WRITE statement, Transfer of control, subscripted variables, DO statement.
SUBPROGRAMMES: Arithmetic function, function Subprogramme, Subroutine Subprogramme.
DECLARATIVE STATEMENTS: the DATA statement, the COMMON statement, the EQUIVALENCE Statement, MATLAB Package

**Text Book :**

FORTRAN 90 for Engineers and Scientists, Larry Nyhoff and Sanford Leestma

**STAT300 SIWES:**

It is a six months practical training course to be undertaken by each student in an industry after the completion of the first
semester of 300 level. The scheme is called Students Industrial Work Experience Scheme (SIWES). At the end of the training,
each student is required to submit a report about what he / she has learnt during this practical industrial training.

**STAT301 -Sampling Distributions and Testing of Hypothesis (3 Credit Units) :**

**Prerequisite – STAT202**
The chi-square, t and F distributions, properties of these distributions and inter-relationship between them. Concept of statistical
hypothesis, null hypothesis, alternative hypothesis (one sided and two sided), level of significance and critical region.
Basic steps of testing hypothesis, simple and composite hypothesis, type I and type II errors, power of a test, Neyman-Pearson
fundamental lemma, Large sample tests such as normal test for testing of proportions and means, applications of chi-square,
t and F distributions in testing of hypothesis.

**Text Books:**

Concepts of Statistical Inference, Guenther, W.C., Mc-Graw-Hill, New York, USA.

Fundamentals of Mathematical Statistics, Gupta S.C. and Kapoor, V.K., Sultan Chand and Sons, New Delhi, India.

**STAT303-Linear Statistical Inference and Analysis of Variance (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
Estimation of regression parameters under linear models, testing of hypothesis about regression parameters. The Gauss-Markoff theorem,
selection of best regression (case of only one predictor variable), analysis of variance (ANOVA), fixed, random and mixed effect models,
assumption underlying ANOVA, one-way, two-way and incomplete three-way classifications, analysis of covariance.

**Text Books:**

Linear Statistical Inference, Rao, C.R., John Wiley and Sons, New York, USA

Fundamentals of Statistics, Vol. II, Goon, A.M., Gupta, M.K., and Dasgupta, B., World Press, Kolkata, India.

**STAT305 – Design and Analysis of Experiments I (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
Basic concepts such as experiment, treatment, experimental unit, experimental error, basic principles, randomization,
replication and local control, the completely randomized design (CRD), randomized block design (RBD) and latin square design (LSD),
layout and analysis, missing plot technique in RBD and LSD, Orthogonal Latin square design, layout and analysis of 2n factorial
experiments carried out in RBD, confounding, simple notion of balanced incomplete block design (BIBD).

**Text Books:**

Fundamentals of Statistics, Vol. II, Goon, A.M., Gupta, M.K., and Dasgupta, B., World Press, Kolkata, India.

Design of Experiments, Kempthorn, O., John Wiley and Sons, New York, USA.

**STAT307 – Advanced Probability Theory I (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
The axiomatic approach to the theory of probability as developed by Kolmogorov, probability inequalities such as Markov’s inequality.
Chebychev’s inequality, Jensen’s inequality and Cauchy-Schwartz inequality, generating functions such as probability generating function,
characteristic function and their properties, inversion theorem, convergence concepts and weak and strong law of large numbers,
various forms of central limit theorem.

**Text Books:**

An Introduction to the Theory of Probability and its Application. Vol I. Feller, W., John Wiley and Sons, New York.

Theory of Probability, Mukhopadhyay, P., New Central Book Agency, Kolkata, India.

**STAT309 – Industrial Statistics - I (3 Credit Units) :**

**Prerequisite – STAT202**
Process Control: Concept of statistical quality control, types of quality measures, control charts for variables and
attributes (x ̅, R) and (x, S) charts, control charts for standard deviation, range, fraction defectives, number of defectives and
number of defects per unit (under standard given and not given for all charts).

Product control: acceptance sampling, basic concepts, producers’ risk and consumers’ risk, acceptable quality level (AQL),
rejectable quality level (RQL), average outgoing quality (AOQ), average outgoing quality limit (AOQL), O.C. function, A.S.N.
functions LTPD and ATI, single and double sampling inspection plans.

**Text Books:**

Quality Control and Industrial Statistics, Duncan, A.J., Richard, D. Irwin Inc. Homewood.

Statistical Quality Control, Grant, E.L., Mc-Graw Hill Book Co.

**STAT311 – Sampling Techniques I (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
Basic concepts, sampling vs complete enumeration, principal steps of a sample survey, probability sampling, purposive sampling
and mixed sampling procedures, simple random sampling (with and without replacement) determination of sample size, stratified sampling,
ratio and regression methods of estimation, systematic sampling, cluster sampling with equal cluster sizes.

**Text Books:**

Sampling Techniques, Cochran, W.G., John Wiley and Sons, New York, USA.

Sampling Theory of Surveys with Applications, Sukhatme, P.V. and Others, Iowa State University Press, Ames, Iowa, USA

**STAT313 – Decision Theory (3 Credit Units) :**

**Prerequisite – STAT102**
Basic Concepts related to a decision problem, states of nature, parametric space, decision space, action space,
randomized and non randomized decisions, pay offs, optimal decision such as maximim, minimax and Bayes decision rules,
decision tree analysis, introduction to the theory of games, saddle point, two-person zero sum game.

**Text Books:**

Statistical Decision Theory, Weiss S., McGraw-Hill Book Co.

Introduction of Statistics and Probability, Dudewicz, E.J., Rinehart & Winston, New York, USA.

**STAT315 – Educational Statistics (3 Credit Unit) :**

**Prerequisite – STAT102**
Scope, nature and use of educational data resources and methods of collection of data related to education, educational indicators
designed for educational information systems, education flow models and performance evaluation, multivariate methods in educational
data analysis, the role of operations research in educational management.

**Text Books:**

Statistics in Psychology and Education, Garret, H.E., Longman, Green (1966) and Vakilis Feffer and Simons (1965)

Fundamentals of Statistics in Psychology and Education, Guilford, J.P., McGraw Hill.

**STAT317 – Biometry II (3 Credit Units) :**

**Prerequisite – STAT204**
Feller’s theorem and fiducial limits. The Behren’s distribution, dilution assays design and criticism of direct assays,
indirect assays, dose-response regression, assay validity, individual effective dose, quantal response, relation between
the individual effective dose and quantal response, Probit transformation, logit transformation.

**Text Books:**

Biometry 3rd edition, Sokal, R. R. & Rohef S., Freeman, W.H. (1994)

Statistical Methods in Biological Assays, Finney, D.J., Charles Griffith and Co. Ltd. London

**MATH311 – Mathematical Modeling (3 Credit Units) :**

**Prerequisite – MATH201**
Methodology of Model building: Identification, formulation and solution of problems. Cause-effect diagrams.
Modeling using graphs and proportionality: modeling by interpolation using polynomials. Modeling using Least
squares and Linear programming. Modeling deterministic behavior and probabilistic processes. Modeling using derivatives:
applications using differential equations.

**Text books:**

1. A first course in Mathematical Modelling, F.R Giordano & M.D. Weir, Woodsworth, Inc. (1985).

2. Mathematical Modeling for Industrial Processes, Lassi Hyvaarinen, Springer-verlag (1970).

3. Mathematical Methods of Operations Research, T.L. Saaty, Dover Publications, Inc. (1988).

**STAT400 – Statistical Project (6 Credit Units) :**

**Prerequisite – STAT300**
Individual work on a selected topic illustrating applications of some of the theories and techniques covered in Statistics.

**STAT401– Non-Parametric Statistical Methods (3 Credit Units) :**

**Prerequisite – STAT301**
Definition, concepts of non-parametric estimation and testing of hypothesis, non parametric tests such as: sign test, runs test,
median test, Mann-Whitney - Wilcoxon test, Wilcoxan signed rank test, Kolmogorov – Smirnov test, Wald - Wolfowitz test,
Cochran Q test, the Friedman test, Kruskal - Wallis test.

**Text Books:**

1. Introduction to the Theory of Non - Parametric Statistics, Randles & Wolfe; John Wiley & Sons Inc., New York, US

2. Practical Non - parametric Statistics, Conover, W.J., John Wiley & Sons Inc.

**STAT403 – Regression Analysis (3 Credit Units) :**

**Prerequisite – STAT303**
Concept of regression and least squares method of fitting of a regression curve, the matrix approach to linear regression,
selecting the best regression equation, multiple linear regression models, polynomial models of various orders,
models involving transformation, non – linear models that are intrinsically linear, use of dummy variables in multiple regression,
introduction to non - linear estimation, partial and conditional regression models, canonical correlation, test of independence of
regression coefficients, Multicollinearity and other problems associated with best Regression models.

**Text Books:**

1. Applied Regression Analysis, Draper, N.R. and Smith, H., John Wiley & Sons Inc. New York, USA

2. Econometric Methods, Johnston, J., McGraw – Hill, Kogakusha Ltd., London.

**STAT405 – Stochastic Processes (3 Credit Units) :**

**Prerequisite – STAT307**
Introduction, definition, basic concepts, Markov chain, transition and absolute probabilities, classification of states,
classification of Markov chain, random walk, random walks in presence of absorbing and reflecting barriers, definition of Markov process,
classification, special Markov process such as birth - death process, birth process and Poisson process, queueing process, its classification,
the simplest queueing process (M/M/1) and waiting time distribution along with simple application.

**Text Books:**

1. A first course in Stochastic Process, Karlin, S., Academic Press, New York, USA.

2. Stochastic Process, Doob, J.L., John Wiley and Sons Inc., New York, USA.

**STAT407 – Design and Analysis of Experiments II (3 Credit Units) :**

**Prerequisite – STAT305**
Split plot and strip plot designs, balanced incomplete block design (BIBD), partially balanced incomplete block design (PBIBD),
the cross over design, lattice design, notion of response surface designs.

**Text Books:**

1. Design of Experiment, Joshi, D.D. Tata - McGraw – Hill.

2. Statistics and Experimental Design, Johnson, N.L. and Leone, F.C., John Wiley & Sons, New York, USA.

**STAT409 – Demography (3 Credit Units) :**

**Prerequisite – STAT102 or equivalence**
The scope and importance of demographic studies, vital events and vital statistics, collection of vital statistics,
Mortality and its measures, the crude death rate and its limitations, age specific death rates, infant mortality rate,
standardized death rates, fertility and its measures, the crude birth rate, general fertility rate, age specific fertility rates,
total fertility rate, standardized birth rates, gross and net reproduction rates, elements of life table.

**Text Books:**

1. Demography, Cox, P.R. Institute of Actuaries, Cambridge University Press, London.

2. Introduction to Demography, Spiegelman, M., Harvard University Press, London.

3. Fundamentals of Statistics, Vol. II, Goon, A.M., Gupta, M.K., and Dasgupta, B., World Press, Kolkata, India.

**STAT411 – Bayesian Inference (3 Credit Units) :**

**Prerequisite – STAT303**
Bayesian estimation technique, prior and posterior distribution, posterior Bayes estimator, loss – function approach,
Bayes risk, Bayes estimator – Bayesian interval estimates, Bayesian tests, prediction problem.

**Text Books:**

1. Introduction to Probability and Statistics from Bayesian View Point, Lindley, D.V., Cambridge University Press.

2. Theory of Games and Statistical Decisions, Blackwell, D. and Girshirk, M.A., John Wiley & Sons Inc., N.Y., USA

3. Introduction to the theory of Statistics, Mood, A.M., Graybill, F.A. and Boes, D.C. McGraw Hill, New York, USA.

**STAT413 – Psychometrics (3 Credit Units ) :**

**Prerequisite – STAT301**
The foundations of mental measurement theory: Measurement in psychology and education. The construction of true and error scores,
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-efficient and their estimation,
some test theory for equivalent measurements, item, sampling in test theory and in research design.

**Text Book:**

1. Psychometric Methods, Guilford J. P., McGraw – Hill.

2. Statistical in Psychology and Education, Garret H. E, Longman Green and Vakils,Feffer and Simons.

**STAT415 – Advanced Probability Theory II (3 Credit Units ) :**

**Prerequisite – STAT307**
Basic theory of sets and set functions, construction and properties of measures, extension theorem, Lebesgue measures,
complete measures, Lebesgue Stieltjes measures, definition and properties of the integral, simple function, measurable functions,
Lebesgue integral, Lebesgue-Stieltjes integral, condition for integrability, Probability as measure, probability space,
theorems related to probability space, random variables as measurable function, distribution of random variables,
convergence of random variables, week convergence, convergence almost everywhere, convergence in mean.

**Text Books:**

1. Introduction to Measure and Probability, Kingman, J.F.C. and Taylor, S. J. Cambridge University Press

2. Probability Theory, Lo'eve, M., Van Nostrand and East-West Press.

**STAT417 – Econometrics (3 Credit Units) :**

**Prerequisite – STAT301**
The nature of Econometrics, relationship between economic variables, roles of econometrics, two variable linear model,
least squares estimators, analysis of variance in regression, two – variable non – linear relationships, relation between three variables,
fitting of regression planes, partial and multiple correlations, intra – class correlation, general linear model, multicollinearity,
generalized least squares, autocorrelation, conventional tests for autocorrelation, The BLUE procedure, lagged variables, simultaneous equation methods, identification problem.

**Text Books:**

1. Econometric Methods, Johnston J., McGraw – Hill, Kogakusha, ltd.

2. Econometrics, Wonnacott and Wonnacott, John Wiley and Sons Inc., New York, USA.

**STAT402 – Multivariate Analysis (3 Credit Units) :**

**Prerequisite – STAT 201**
Multivariate data structure, the multiple and partial regression and correlation, multivariate normal distribution,
the marginal and conditional distribution, Hotellings T2 and Mahalanobis D2 distribution, the Wishart distribution,
concept of canonical correlation, discriminant function. Principal components and cluster analysis.

**Text Books:**

1. An Introduction to Multivariate Analysis, Anderson, T.W. John Wiley & Sons Inc., New York, USA.

2. Multivariate Analysis, Dillon and Goldsletein, John Wiley & Sons Inc., New York, USA.

**STAT404 – Time Series Analysis (3 Credit Units) :**

**Prerequisite – STAT303**
Concept of time series, its components such as secular trend, seasonal and cyclic components, random components and various measures of these components,
harmonic analysis, serial correlation and correlogram, stationary time series, correlation between two time series, lag correlation, forecasting in time series.

**Text Books:**

1. Applied General Statistics, Croxton and Cowden, Prentice Hall.

2. The Statistical Analysis of Time Series, Anderson, T.W. John Wiley & Sons Inc., New York, USA

3. The Advanced Theory of Statistics, Vol. 3, Kendal, M.A. and Stuart, A. Charles Griffin and Co. Ltd., London.

**STAT406 – Sampling Techniques II (3 Credit Units) :**

**Prerequisite – STAT311**
Sampling with varying probabilities (with and without replacement), procedure of selecting a sample with varying probabilities,
estimation of population mean and variance and their sampling variances. The two stage and multistage sampling schemes
with equal first and second stage units multivariate ratio estimation, double sampling.

**Text Books:**

1. Sampling Theory of Surveys with Application, Sukhatme, P.V. and others, Iowa State University Press, Ames, Iowa, US.

2. Sampling Techniques, Cochran, W.G., John Wiley and Sons Inc., New York, USA.

**STAT408 – Statistical Inference (3 Credit Units) :**

**Prerequisite – STAT201**
Theory of point estimation, methods of estimation such as method of moments, method of maximum likelihood and method of least squares,
properties of point estimators: unbiasedness, consistency, efficiency, Cramer - Rao inequality and its extension, sufficiency,
Fisher – Neyman criterion and factorization theorem, concept of completeness, Rao - Blackwell theorem, Interval estimation.

**Text Books:**

1. Introduction to Mathematical Statistics, R. V. Hogg & A. T. Craig, Amerind

2. Introduction to the theory of Statistics, Mood, A.M., Graybill, F.A. and Boes, D.C. McGraw Hill, New York, USA.

**STAT412 – Operations Research (3 Credit Units). :**

**Prerequisite – MATH311**
Classical methods of optimization, Maxima and minima, Lagranges’ multipliers. Linear programming: Convex sets and functions,
simplex and revised simplex methods, duality theory, applications. Linear programming applications to diet problems,
transportation problems, manufacturing problems, Network Analysis, etc.

**Text Books:**

1. Operations Research, Sharma, J.K., Macmillan India.

2. Operations Research, Swaroop, Gupta, P.K. and Mohan, M., Sultan Chand and Sons, New Delhi, India.

**STAT414 – Actuarial Science (3 Credit Units) :**

**Prerequisite – MATH311**
The time value of money, compound interest and discounting, present value and accumulated values of streams of payments,
decremental rates and other indices, annuities and sinking funds, solving equation of value, investment and appraisal techniques,
analysis of experimental data and derivation of exposed to risk formulae, graduation method and its application to curve fitting.
Construction of mortality, sickness, multiple decrements and similar tables with applications to life insurance, national social security and pension schemes.

**STAT416 – Industrial Statistics II (3 Credit Units) :**

**Prerequisite – STAT309**
Special process control procedures, concept of reject – limits, modified control limits relationship between control chart limits and specification limits,
charts for subgroup totals and individual measurements, control charts for medians, specification and tolerances aspects.

Acceptance sampling: the multiple and sequential sampling, Dodge-Romig system for lot by lot inspection, acceptance sampling by attributes, some basic aspects of life testing and reliability.

**Text Books:**

1. Statistical Quality control, Grant, E.L., McGraw – Hill Book Co. Ltd.

2. Quality Control and Industrial Statistics, Duncan, A.J. and Richard D., Irwin Inc. Homewood

**STAT165 – Statistics for Social Science (3 Credit Units) :**

**Prerequisite – O/Level Maths**
Nature of statistics, its definition, sources and importance. Methods of data collection and presentation.
Sampling procedures (simple random sampling, systematic sampling, stratified sampling, cluster sampling, e.t.c.).
index numbers, frequency distribution, Measures of central tendency, measure of variation, simple correlation and
regression.

**Text Books:**
1. Statistics for Fresh Undergraduates, Yahaya A., Nnamani C.N., ABU press (2013), Zaria.

2. A basic course in Statistics, G.M. Clerk & D. Cooke, Edward Arnold Ltd. (1978)

**STAT261 – Elements of Statistics (2 Credit Units) :**

**Prerequisite – O/Level Mathematics**
Basic concept of Hypothesis testing, the power of a test, point and interval estimation (Testing and estimation in
large samples and in some standard small samples situations) Discrete and continuous random variable, probability
density functions; binomial, poisson, normal. Contingency tables, Goodness of fit tests.

Basic concepts of sampling, Relationship between normal distribution, student’s, chi-square and f-distributions.
Sampling distributions of the mean and variance with known and unknown standard deviation.

**Text Books:**

1. Statistics for Fresh Undergraduates, Yahaya A., Nnamani C.N., ABU press (2013), Zaria.

2. Statistical Inference I Concepts and Applications H. Frank and S.C. Althoen. Cambridge University Press (1995)

3. An introduction to Probability Theory and its Applications, William Feller

**STAT343 – Statistics (2 Credit Units) :**

**Prerequisite – STAT 102 or equivalence**
Probability as a function of sample space, laws of probability, conditional probability, Bayes’ rule.
Random variables, Mathematical Expectation, computation of the mean and variance of common probability
mass functions using the methods of expectations and methods of moments. Probability distributions of
discrete and continuous random variables. Chebyshe’s inequality, bivariate, marginal and conditional
distributions and moments.

**Text Books:**

1. Introduction to statistics 2nd Edition, R.E Walpole, Jhon wiley and sons (1977)

2. Modern Mathematical Statistics, E.J. Dudeweiz & S.N. Mishra.

3. Introduction to Mathematical Statistics, 3rd Edition R.V. Hogg & A.T Craig, Prentice Hall (1955)

**STAT443 – Design and Analysis of Experiments and Quality Control (2 Credit Units) :**

**Prerequisite – STAT343**
Basic concepts of experimental design, one-way, two-way ANOVA, CRD, RCBD, LSD, GLS. Estimation of missing values,
simple factorial experiments. Process control, Product control, comparison of different sampling plans,
Floating-point arithmetic. Acceptance Sampling, Inspection by attributes, the OC curve, Sampling and their section.
Inspection by variables. Test of significance in quality control. Reliability and life testing.

**Text Books:**

1. Experimental Design 2nd Edition. W.H. Cochran & G.M. Cox, John Wiley & Sons (1957).

2. Introduction to Design and Analysis 2nd Edition, University of California, Berkely, W.H. Freeman (1992).