MATH 248 - Mathematical Statistics

This course is concerned with several fundamental topics in advanced
statistical theory, which include distribution theory, theory of parameter
estimation, hypothesis testing, statistical inference, analysis of variance,
and regression. Since these theoretical tools are of interest in a host of
practical applications, ranging from engineering, control theory and
simulation, to actuarial sciences and econometrics, some concrete
applications will also be discussed in the course. Here are some situations
where the above statistical methods can be used to analyze real-world
problems:

(1) Studying the effects of the presence of four different sugar solutions
(glucose, sucrose, fructose, and a mixture of the three) on bacterial
growth.

(2) Some defendants in criminal proceedings plead guilty and are sentenced
without a trial, whereas others who plead innocent are subsequently found
guilty and then are sentenced. In recent years, legal scholars have
speculated as to whether sentences of those who plead guilty differ in
severity from sentences for those who plead innocent and are judged guilty.
Do historical data suggest that the proportion of all defendants in both
groups who are sent to prison is different for the two groups?

(3) A statistics professor suspects that one of his graders is not properly
grading the weekly quizzes taken by his students. In fact, the professor
suspects that the grader assigns scores at random, unlike his other graders.
Can you device a statistical test that will help in deciding (based on
knowing the scores of all quizzes throughout the entire semester by all
graders) whether the professor's suspicion is justified?