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# CHANCELLOR Sir George Alleyne OCC, MD, FRCP, FACP (Hon), Hon. DSC (UWI) - page 114 / 136

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The

FA C U L T Y Faculty

BOOKLET 2004 – 2005 of Science & Agriculture

MATH 2190 (M 25C) PROBABILITY AND STATISTICS I (4 credits)

MATH 2200 (M 25D) PROBABILITY AND STATISTICS II (4 credits)

Prerequisite:MATH 1140 and MATH 1150 (M 12A and M 12B) or Permission of the Head of DepartmentAnti-requisite: MATH 2140

Prerequisite:MATH 1140, MATH 1150 and MATH 2190 (M 12A, M 12B and M 25C) or Permission of the Head of DepartmentAnti-

and MATH 2150 Syllabus:

(M 25A and M 25B)

Foundations of Probability, basic discrete and continuous dis- tributions; expectation. Joint distribution of several discrete and continuous random variables. Covariance and correlation. The Central Limit Theorem. Basic ideas of point and Interval Estimation. Maximum likelihood Estimation Type I and Type II errors, significance level and power. Hypothesis of means, variances and proportions. Regression Analysis (mainly simple linear regression). Experimental Design. One and two-way ANOVA. Basic ideas of sampling from finite populations.Comment:MATH 2190 (M 25C ) is a four (4) credit alternative to both MATH 2140 ( M 25A) and MATH 2150 (M

25B) and is primarily aimed at non-Mathematics Majors.

Examination: One 2-hour paper

60%

Coursework

40%

requisite: MATH 2140 and MATH 2150 (M 25A and M 25B) Syllabus: Probability Theory: Conditional expectation for discrete ran- dom variables, Bayes Theorem, transformations of one ran- dom variable, evaluation of probabilities of events for continu- ous bivariate random variables transformations of two ran- dom variables, the squared distributions, moment generating functions; proof of the Central Limit Theorem, Markov and Chebychev inequalities, the weak law of large numbers. Sta- tistical Inference: Unbiasedness, Fisher information and the Cramer-Rao inequality (without proof), sufficiency, the Fisher factorisation criterion, the Neyman-Pearson lemma. Statisti- cal Methods: Factorial designs; non-parametric rank methods, the sign test, squared rank test, rank sum test, Kruskal-Wallis test, goodness of fit tests. Sampling Theory of Surveys: Simple random samples, stratified samples, ideas underlying other sampling schemes, non-sampling sources of error including

non-response and poor sampling design. Examination: One 2-hour paper Coursework

60% 40%

MATH 2210 (M 29A) MATHEMATICS OF FINANCE (4 Credits)

Prerequisite: MATH 1140 and MATH 1150 (M12A and M12B) Syllabus: Introduction to actuarial science; measurement of interest; solutions of problems in interest, basic annuities; more gen- eral annuities, yield rates, amortisation schedules and sinking funds, bonds and other securities, practical applications.

Examination: hour written paper

One 2- 70%

Coursework

30%

114

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