STAT 342.3 Mathematical Statistics, Fall 2007

Longhai Li, Department of Mathematics and Statistics, University of Saskatchewan

Description

First of all, Statistical Mathematics or Probability Theory is a more appropriate name for this course. This course deals with basic probability concepts at a moderately rigorous level. It aims at equipping the students with necessary tools in deriving distributions of various random variables in statistics and solid knowledge in standard distributions. Topics include probability spaces, conditional probability and independence, discrete and continuous random variables, standard probability models, expectations, moment generating functions, sums and functions of random variables, sampling distributions, asymptotic distributions.

Course outline: PDF

Lecture Notes

Lecture #Time PDF fileContent descriptionSections in textbook
Lecture 1Sept 6 2007 PDFProbability AxiomSection 1.1-1.3
Lecture 2Sept 11 2007 PDFBasic Properties of Probability based on Probability Axiom. Section 1.4
Lecture 3Sept 13 2007 PDFConditional Probability. Section 1.5
Lecture 4Sept 18 2007 PDF Total Probability, Bayes Rule, Counting Technique (permuation, combination, group). Section 1.5, 1.6
Lecture 5Sept 20 2007 PDF Function, Derivative, Integral, Random Variable, CDF, PMF, PDF.Section 2.1-2.3
Lecture 6Sept 25 2007 PDF More on PDF, Mixed Random Variable, PDF of Transformation of Single Random Variable. Section 2.3, 6.2,6.3
Lecture 7Sept 27 2007 PDF Random Vector, Joint Distribution for Discrete Random Variables. Section 4.2
Lecture 8Oct 2 2007 PDF Joint Distribution for Continuous Random Variables, Examples of Joint Distributions: IID, Markov chain, Bayesian Network. Section 4.3-4.6
Lecture 9Oct 4 2007 PDF PDF of Transformation of Random Vector, Deriving Distributions of Sum, Ratio and Ordered Statistics.Section 6.3,6.4,6.5
Lecture 10Oct 9 2007 PDF Expected Value and Conditional Expected Value. Section 2.4,5.2,5.4
Lecture 11Oct 11 2007 PDF Variance, Inner Product, Cauchy-Schwartz Inequality,Correlation, and their Properties. Section 5.3
Lecture 12Oct 16 2007 PDF Markov Inequality, Chebychev's Inequality, Moments, Improper Integrals, Concave Function, Jensen Inequality. Section 2.4
Lecture 13Oct 18 2007 PDF More on Jensen Inequality, Moment Generating Function, Characteristic Function. Section 2.5,5.5,6.4
Lecture 14Oct 25 2007 PDF Multinomial distribution for n=1 (Multiway distribution). Section 3.2
Lecture 15Nov 13 2007 PDF Multinomial distribution for n>1, distribution of proportion, p-value. Section 3.2
Lecture 16Nov 15 2007 PDF Hypergeometric distribution (Section 3.2), Gamma distribution and inverse Gamma distribution. Section 3.3
Lecture 17Nov 20 2007 PDF Beta distribution, F distribution Section 8.4
Lecture 18Nov 22 2007 PDF Normal distribution and Multivariate normal distribution.Section 8.3
Lecture 19Nov 27 2007 PDF Statistical inference in normal samples. Section 8.3
Lecture 20Nov 29 2007 PDF Convergence in distribution and probability, CLT, WLLN Chapter 7

Assignments

  1. Assignment 1: PDF, Postscript

    (Correction to Question 5: choosing 2 items from 4 items only)

  2. Assignment 2 and 3: PDF, Postscript

  3. Assignment 4: PDF, Postscript

    Scanned pages from textbook is included in the above file

  4. Assignment 5: PDF, Postscript

  5. Assignment 6: PDF, Postscript

  6. Assignment 7: PDF, Postscript

  7. Assignment 8: PDF, Postscript

  8. Assignment 9: PDF, Postscript

  9. Assignment 10: PDF, Postscript

Midterm

A non-programmable caculator is allowed. The test is available: PDF, Postscript

Final

STAT 342 01 December 17 9:00 a.m. EDUC 3301

A non-programmable caculator is allowed, and a cheating sheet will be provided. Here is the cheating sheet (PDF) for the final exam.

Additional Handout

Pre-Class Quiz: PDF, Postscript

PMF and CDF of some Binomial distributions: PDF, Postscript

R Codes

Small R program for looking at order statistics, the plots of X_(30) and X_(70) when the number of original random variables is 100 and have uniform(0,1) distribution are here: PDF, Postscript.
Return to Longhai Li's homepage