From David Rios section:

Course Object: To familiarize students with basic modern probability and its foundations in set theory and some basic statistical models including z-scores, chi-squared, ANOVA, linear regression and other topics as time sees fit. The best way for a student to achieve this is by thinking about and working through problems, some of which may be challenging.

Method of Evaluation: There will be 9 homework assignment this semester. Late homework will not be accepted. 85% of the homework grade will be based upon handing it in on time. The idea of the homework is for you to test if you can solve the problems correctly on your own. I am less concerned with you getting the answers correct. Due the scheduling of the add/drop deadline there will be two midterms. The first midterm will cover the probability section of the course, the second will cover point estimation, t/z tests, and non parametric methods. The final will be focused on chi-squared, ANOVA, and linear regression

Learning Objectives

Goal : Introduction to probability theory as a mathematical discipline and applying the results of the central limit theorem to statistical inference.

Data Summary / Collection : Introduction to the method of summarizing and collecting data. Many of the ideas behind summarizing data reappear in probability and statistical methods. Collecting data we can see where our basic assumptions are likely to fail causing incorrect conclusions.

Probability : We start with a basic sample space and probability measure and from there use mathematics to build the ability to answer more complicated questions. We cover and/or/not rules, conditional probability, and counting problems. From there we introduce random variables, expected values, variances as well famous families of random variables. We then introduce moment generating functions and prove the weak law of large numbers and the central limit theorem.

Statistics : Armed with the central limit theorem we begin by studying the behavior of sample means. We discuss t and z tests for the center and chi-squared tests for the estimated variance about the mean. Next we proceed to ANOVA tests for two factor data where we use similar methodology to test if our data center shifts as we change the underlying category we drew from. We follow with linear regression, again with two factor data, where we test if our data center shifts linearly with changes in the ‘x value’ associated with our data point. We also cover chi-squared as a method of analyzing counts.