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Transcript
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