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CHANCELLOR Sir George Alleyne OCC, MD, FRCP, FACP (Hon), Hon. DSC (UWI) - page 115 / 136

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The

FA C U L T Y Faculty

BOOKLET 2004 – 2005 of Science & Agriculture

MATH 2220 (M 29B) INTRODUCTION TO ACTUARIAL MATHEMATICS (4 Credits)

MATH 3120 (M 31B) MATHEMATICAL STATISTICS – STATISTICAL INFERENCE (4 Credits)

Prerequisite: MATH 2120, MATH 2140 and MATH 2210 (M 21A, M 25A and M 29A) Syllabus: Survival distributions and life tables, utility theory, life insur- ance, life annuities, commutation functions, net premiums and premium reserves, introduction to multiple life functions.

Examination:

One 2-hour written paper

70%

Coursework

30%

MATH 3110 (M 31A) MATHEMATICAL STATISTICS – PROBABILITY THEORY (4 Credits)

Prerequisite: MATH 2120 (M 21A) or permission of the Head of Department Syllabus: Basic Probability rules, including Bayes’ rule, theorem on total probability; Conditional Probability; Random Variable; Math- ematical Expectation; means, variance; Covariance of variables. Variance of sum of n random variables Chebychev’s theorem; Standard density functions and mass functions; Moment gen- erating function. Random sample; some important statistics, sampling distributions. Central limit theorem. Transformations of several random variables; order statistics; conditional ex- pectation; the bivariate and multivariate normal distributions.

Examination:

One 2-hour written paper

60%

Coursework

40%

Prerequisite: MATH 3110 or MATH 2140 (M 31A or M 25A) Syllabus: Theory of Estimation: Ideas of point estimation; mean-squared error; interval estimation; method of maximum likelihood; Cramer-Rao Inequality. Hypothesis Testing: Type I and Type II errors; tests concerning means, variances and proportions; Goodness of fit Tests; non-parametric tests. Ideas of Regres- sion Analysis including simple linear Regression in detail; Ex- perimental Design and the Analysis of Variance (Completely Randomised Design, Block Designs, Latin Squares, Factorial Designs). Efficiency and the Fisher-Factorisation Criterion; the Rao-Bla ckwell theorem.Estimation from multinomial popu- lations. Simple random, stratified, cluster and systematic sam- pling; non-sampling errors in surveys ; likelihood ratio tests.

Examination:

One 2-hour written paper

60%

Coursework

40%

MATH 3240 (M 31S) REAL ANALYSIS (4 credits)

Prerequisite: Syllabus:

MATH 2120 (M 21A)

Properties of real numbers, real line topology (open sets, clus- ter points, compactness, connectedness). Introduction of to- pological spaces. Mectric space. Continuity and homoeomorphism. Point wise and uniform convergence of se-

quence and series of real valued functions. Examination: One 2-hour written paper Coursework

75% 25%

115

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