MT427 Mathematical Statistics
Spring 2011

Prof.  Dan Chambers  
Office:  365 Carney
617-552-3769 (email is more reliable)

Mathematical Statistics is a continuation of MT426 Probability or an equivalent (calculus-based) probability course. Whereas probability takes a given distribution and calculates the probability of seeing certain data values, statistics takes data and attempts to find the distribution that generates it, estimate parameters of the underlying distribution, and test hypotheses about those parameters.

Some of the topics we'll be covering this semester are: the central limit theorem, maximum likelihood estimation, method of moments estimation, confidence intervals, minimum-variance estimators, Cramer-Rao lower bound, sufficiency and consistency of estimators, hypothesis testing: binomial parameter, t test, Z test, generalized likelihood ratio, inferences about variances, two sample problems, goodness-of-fit tests, tests of independence and homogeneity, and nonparametric statistics.

Here is a link to the syllabus.

Here is a review of probability and some of the important distributions and their properties.

Office Hours: Mondays 12-1, Wednesdays 9-10, Fridays 3-4, or by appointment.

The text we'll use is An Introduction to Mathematical Statistics and Its Applications, 4th Edition, by Richard Larsen and Morris Marx. We'll finish chapter 4, then cover chapters 5-7, 9, 10, and some of 14.

Jan. 17-20
MLK Day 5.1 MLE introduction 5.2 MLE examples
HW1 assigned (due January 28)
Jan. 24-28
5.2 more MLE
 5.2 more MLE
MOM estimates
5.3 confidence intervals
HW1 solutions
Jan. 31-
Feb. 4
class canceled
5.3 more confidence intervals
5.4 unbiasedness
Feb. 7-11
5.5 CRLB
5.5 MVUE's
HW2 solutions
5.6 sufficiency
Feb. 14-18
5.6, 5.7 consistency
6.2 intro to hypothesis testing
HW3 solutions
Feb. 21-25
Exam 1
intro continued hyp. testing: means (known variance)
Feb. 28-
Mar. 4
hyp. testing: proportions (started) proportions (finished), P-values Type I and II errors, power
Mar. 7-11
spring break
spring break
spring break
Mar. 14-18
more on alpha, beta, power: sample size non-Normal data
hyp. test vs CI
estimators for mu, sigma Normal
gamma function review
Mar. 21-25
Chi Square distribution properties
CI and hyp test for normal variance
F and t distributions F and t distributions
Mar. 28-
Apr. 1
t test and CI's for means
HW4 solutions
two sample t test for means two sample test for variances
Apr. 4-
Apr. 8
two sample test for proportions
HW5 solutions
Exam 2
multinomial distributions
Apr. 11-15
goodness of fit- known parameters
goodness of fit-unknown parameters
more examples
Apr. 18-22
Patriot's Day
intro to contingency tables
HW7 solutions
Easter break
Apr. 25-29
Easter break Chi square test for independence
sign test
May 2-6
Wilcoxon signed rank test
runs test for randomness