MATH 370 Syllabus

Probability and Statistics I

Revised: March 2024

Course Description

Classical probability models, distributions of discrete and continuous random variables, joint probability distributions, mathematical expectation.

 Prerequisite: MATH 255

Student Learning Objectives

 By the end of the course, students should be able to

1. Set up and evaluate simple probability statements
2. Calculate means, variance and covariance of random variables
3. Describe and evaluate probabilities associated with uniform, binomial, hypergeometric and Poisson distributions for discrete random variables
4. Develop and evaluate and probabilities associated with uniform, normal, gamma, exponential, chi-squared and Weibull distributions for continuous random variables
5. Make statistical inferences based on sampling

Text

Wackerley, Dennis, Mendenhall, William., and Scheaffer, Richard. Introduction to Mathematical Statistics with Applications, Seventh Edition. Brooks/Cole Cengage, 2008.

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Course Outline

• Chapter 1: What Is Statistics? (0.5 week)
  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 (2.5 weeks)
  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 (3 weeks)
  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. (Note: Sections 3.6 and 3.9-3.11 are optional.)

• Chapter 4: Continuous Variables and Their Probability Distributions (2.5 weeks)
  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. (Note: Sections 4.8-4.9 are optional.)
• Chapter 5: Multivariate Probability Distributions (3.5 weeks)
  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. (Note: Sections 5.10-5.11 are optional.)