Introduction to STAT 414. Printer-friendly version As the title of Stat 414 suggests, we will be studying the theory of probability, probability, and more probability throughout the course. Here's a (brief!) Overview of what we'll do in the course: In Section 1, one of our primary focuses will be to develop an understanding of the various ways in which we can assign a probability to some chance event. We'll also learn the fundamental properties of probability, investigate how probability behaves, and learn how to calculate the probability of a new chance event. In Section 2, we'll explore discrete random variables and discrete probability distributions. In Section 3, as the title suggests, we will investigate probability distributions of continuous random variables, that is, random variables whose possible outcomes fall on an infinite interval.
In Section 4, we'll extend many of the definitions and concepts that we learned in Sections 2 and 3 to the case in which we have two random variables. Lesson 1-6: The Big Picture. Lesson 1: The Big Picture Printer-friendly version Introduction In this lesson, our primary aim is to get a big picture of the entire course that lies ahead of us. Along the way, we'll also learn some basic concepts to help us begin to build our probability tool box. Lesson 7-12: Discrete Random Variables. Lesson 13-17: Exploring Continuous Data. Printer-friendly version Introduction In the beginning of this course (in the very first lesson!)
, we learned how to distinguish between discrete and continuous data. Lesson 18-21: Distributions of Two Random Variables. Printer-friendly version Introduction As the title of the lesson suggests, in this lesson, we'll learn how to extend the concept of a probability distribution of one random variable X to a joint probability distribution of two random variables X and Y. In some cases, X and Y may both be discrete random variables. For example, suppose X denotes the number of significant others a randomly selected person has, and Y denotes the number of arguments the person has each week. We might want to know if there is a relationship between X and Y. In some cases, X and Y may both be continuous random variables. Objectives. Lesson 22-28: Functions of One Random Variable. Lesson 29-36: Point Estimation. Printer-friendly version Introduction Suppose we have an unknown population parameter, such as a population mean μ or a population proportion p, which we'd like to estimate.
For example, suppose we are interested in estimating: p = the (unknown) proportion of American college students, 18-24, who have a smart phoneμ = the (unknown) mean number of days it takes Alzheimer's patients to achieve certain milestones In either case, we can't possibly survey the entire population. In this lesson, we'll learn two methods, namely the method of maximum likelihood and the method of moments, for deriving formulas for "good" point estimates for population parameters. Objectives. Lesson 37-43: Tests About Proportions. Lesson 44-50: Chi-Square Goodness-of-Fit Tests. Lesson 52: Probability, Estimation, and Concepts. Lesson 53-57: Sufficient Statistics.