Revised: February, 2015
Classical probability models, distributions of discrete and continuous random variables, joint probability distributions, mathematical expectation. Prerequisite: MATH 255. Three semester hours.
By the end of the semester, students will be able to
Wackerley, Dennis, Mendenhall, William., and Scheaffer, Richard. Introduction to Mathematical Statistics with Applications, Seventh Edition. Brooks/Cole Cengage, 2008.
Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Chapter 1: What Is Statistics? (2 days)
Introduction. Characterizing a Set of Measurements: Graphical Methods. Characterizing
a Set of Measurements: Numerical Methods. How Inferences Are Made. Theory and Reality.
Summary.
Chapter 2: Probability (7 days)
Introduction. Probability and Inference. A Review of Set Notation. A Probabilistic
Model for an Experiment: The Sample-Point Method. Tools for Counting Sample Points.
Conditional Probability and the Independence of Events. Two Laws of Probability. Calculating
the Probability of an Event: The Event-Composition Method. The Law of Total Probability
and Bayes’ Rule. Numerical Events and Random Variables. Random Sampling. Summary.
Chapter 3: Discrete Random Variables and Their Probability Distributions (7 days)
Basic Definition. The Probability Distribution for a Discrete Random Variable. The
Expected Value of a Random Variable or a Function of a Random Variable. The Binomial
Probability Distribution. The Geometric Probability Distribution. The Negative Binomial
Probability Distribution. The Hypergeometric Probability Distribution. The Poisson
Probability Distribution.
Moment and Moment-Generating Functions. Probability-Generating Functions. Tchebysheff's
Theorem. Summary.
Chapter 4: Continuous Variables and Their Probability Distributions (7 days)
Introduction. The Probability Distribution for a Continuous Random Variable. Expected
Values for Continuous Random Variables. The Uniform Probability Distribution. The
Normal Probability Distribution. The Gamma Probability Distribution. The Beta Probability
Distribution. Some General Comments. Other Expected Values. Tchebysheff's Theorem.
Expectations of Discontinuous Functions and Mixed Probability Distributions. Summary.
Chapter 5: Multivariate Probability Distributions (10 days)
Introduction. Bivariate and Multivariate Probability Distributions. Marginal and Conditional
Probability Distributions. Independent Random Variables. The Expected Value of a Function
of Random Variables. Special Theorems. The Covariance of Two Random Variables. The
Expected Value and Variance of Linear Function of Random Variables. The Multinomial
Probability Distribution. The Bivariate Normal Distribution. Conditional Expectation.
Summary.
Chapter 6: Functions of Random Variables (5 days)
Introduction. Finding the Probability Function of a Function of Random Variables.
The Method of Distribution Functions. The Method of Transformations. The Method of
Moment-Generating Functions. Multivariable Transformations Using Jacobians. Order
Statistics. Summary.
Chapter 7: Sampling Distributions and the Central Limit Theorem (4 days)
Introduction. Sampling Distributions Related to the Normal Distribution. The Central
Limit Theorem. A Proof of the Central Limit Theorem (Optional). The Normal Approximation
to the Binomial Distribution. Summary.