Development of probability theory with emphasis on how probability relates to statistical inference.
Topics include review of probability basics, counting rules, Bayes Theorem, distribution function,
expectation and variance of random variables and functions of random variables,
moment generating function, moments, probability models for special random variables,
joint distributions, maximum likelihood estimation, unbiasedness, distributions of functions of random
variables, chi-square distribution, students t distribution, F distribution, and sampling distributions
of the sample mean and variance. Prerequisite:
STA 261,
STA 301, or
STA 368. Corequisite:
MTH 251
Section B: Syllabus
Section C: Syllabus
Some set theoretic proofs
Some combinatoric proofs
Kurtosis
Moment generating function
Binomial Distribution
Geometric Distribution
Transformation of Diameter of of sphere to Volume
More transformations of random variables
PDF and MGF for some random variables
Maximum Likelihood Estimation
More Maximum Likelihood Estimation
Introduction to Bayes model
Conjugate normal Bayes model
Distribution sheet for final exam
Bayesian inference
Be sure to bring a calculator to the final exam
Last updated April 28, 2009