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NASSAU COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS, COMPUTER SCIENCE & INFORMATION TECHNOLOGY Course Outline for MAT 131 Probability with Statistical Inference Curriculum Interdisciplinary Lab hours None Semesters offered Indicated in Catalog Length of semester 15 Weeks Class hours 3 Credits 3 Text John Freund’s Mathematical Statistics with Applications, 7th ed., by Miller and Miller. Published by Prentice Hall PREREQUISITE MAT l23 CATALOG DESCRIPTION Probability as a mathematical system: sample spaces, probability axioms, and simple theorems, permutations, combinations, Bayes theorem, random variables; discrete and continuous probability and distribution functions: binomial, hypergeometric, Poisson, and normal distributions, methods of estimation and hypothesis testing MATH CENTER REQUIREMENT As part of this course, students should avail themselves of further study and/or educational assistance available in the Mathematics Center: B-l30 and B-l26. These activities and use of the resources provided are deemed an integral part of the course, and will help the student master necessary knowledge and skills. OBJECTIVES General This course is designed to introduce the basic concepts of probability and statistics. Its aim is the understanding of the nature, scope and theoretical basis of probability with statistical inference. Specific Based on a strong foundation in probability, some of the fundamental concepts of statistical inference are introduced. Studying discrete and continuous populations involving the binomial, hypergeometric, and normal distribution, and then examining some sampling techniques accomplish this. TOPICS I. Introduction: Combinational methods and binomial coefficients. II. Probability: Sample spaces events; probability of events; conditional probability, Bayes’ Theorem. III. Probability distributions: Discrete and continuous random variables-probability density functions, multivariate, distributions. IV. Mathematical expectation: Expected value; moments; Chebyshev’s theorem; moment generating functions. V. Special probability distributions: discrete, uniform, hypergeometric, Poission and multinomial distributions. Bernoulli, binomial, VI. Special probability densities: uniform density, gamma, exponential, chi-square, beta and normal distributions. VII. Functions of random variables: distribution function, technique transformation of variable technique, moment generating function technique. VIII Sampling distributions: the distribution of the mean, chi- square and t-distributions. COURSE OUTLINE Topic Chapter Introduction 1 Probability 2 Probability Distributions and Probability Densities 3 Mathematical Expectation 4 Special Probability Distributions 5 Special Probability Densities 6 Functions of Random Variables 7 Sampling Distributions 8 Estimation Theory 10 Sections 1, 2, 3 1, 2, 3, 4, 5, 6, 7, 8 1, 2, 3, 4, 5, 6, 7 1, 2, 3, 4, 5, 8 3, 4, 5, 8 1, 2, 3, 4, 5, 6, 7, 8, 9 1, 2, 3, 4, 5, 6, 7 1, 2, 3 1, 2, 3, 4, 5 1, 2, 3 REFERENCES l. Probability & Statistics for Engineers & Scientists, 7th ed., by Walpole, et. al. PrenticeHall, 2002. 2. Introductory Probability & Statistical Applications, 2nd ed. by Meyer & Meyer, Addison Wesley. 3. Introduction to Mathematical Statistics, 5th edition, by Hogg & Craig, Prentice Hall, 1994. 4. An Introduction to Probability Theory and it’s Applications, Volumes I & II, by Feller, Wiley. 5. Introduction to Probability Models, 7th ed., by Ross, Academic Press, 2000. DATE LAST REVISED: Summer, 2016