Statistics 3657a Handouts Page

The Greek alphabet and the pronunciation of these letters

http://en.wikipedia.org/wiki/Greek_alphabet

September 5, 2014 Ch1-Sect-2-3-5.pdf

Sept 8, 2014 urn-eg-1.pdf

Sept 10, 2014 : Ch1-6.pdf

Sept 10, 2014 : chap2-1.pdf properties of cdf

Sept 12, 2014 chap2-2.pdf properties of pdf = probability density function

Functions of a single r.v. Chap2-3-discrete.pdf and ch2-3.pdf

Sept 16, 2014 : TaylorSeries.pdf

Sept 17, 2014 : For next lecture chap3-1.pdf

Sept 19, 2014 : ch3-3-eg1.pdf Some parts of this handout will be used later for Section 3.5 conditional distributions.

Sept 24, 2014 Ch3-3and4.pdf this and the previous handout will be used over the next few lectures. (this is updated with one extra page Sep 26, 2014)

Sept 26, 2014 : bivariate normal.pdf

Sept 29, 2014 : Ch3-5.pdf conditional probability ; one section deals with a special case and a mixture distribution. Rscript to plot densities of normal mixture Handouts\mxiture-eg.R

October 1, 2014 : last year's term test 1 OCT-2013.pdf The first term test is next week. Solutions will not be posted for the old test.

October 3, 2014 : chap3-6.pdf

The first term test will cover the material up to the beginning of Chapter 3, Section 3.6.1 sums of r.v.s, not the ratio of r.v.s. It also covers all the material in the handouts, some of which are extensions of the material in the test.

A formula sheet will be given for the test formulae.pdf

October 8, 2014 : ratio-unif.pdf (first part of this handout, the rest will be used later) and RatioNormals.pdf

October 10, 2014 : AETaylor-AdvancedAclculusIntegralTransformTheorem.pdf Jacobians for change of variable in integrals; note there are conditions required for this to be valid

Continue with the material for Chapter 3.6

Also see ratio of uniforms handout and t-ratio.pdf (derivation of distribution for Student's t- statistic.

October 15, 2014 : I thank several students for their finding of some typos in the handouts. These have been corrected and reposted.

orderstats.pdf These are useful in several areas of statistics, finance are reliability theory. Later in the course we will see how these are used to construct QQ plots, in particular qqnorm which is commonly used as a diagnostic tool in statistics and also in finance to decide if returns data are heavy tailed. The transformations are many to one mappings.

October 20, 2014 : Ch4_Expectation.pdf

Oct 21, 2014 : some integrals over -infinity to +infinity are not defined. Here is an example and a discussion about this issue integral2.pdf based on one of our earlier examples.

October 24, 2014 : expectation examples see Oct 20 handout and the order statistics example Oct 15.

Oct 27, 2014 : Finish expectation handout material. Conditional expectation : Ch4-4-cond-expec.pdf (a couple of paragraphs added in the introductory part)

topic after conditional expectation Section 4.5 moment generating functions MGF.pdf (update and some typos corrected Nov 3, 2014) and MGFtable.pdf

Oct 29, 2014 : Oct2014-PartialSolutions.pdf and histogram Oct2014hist.pdf

Nov 3, 2014 : SuggestedProblemsChapter3and4.pdf

Nov 5, 2014 : Test II from November 2013 Nov2013.pdf; this is the partial solution as given out last year after the test.

The test will cover material since the first term test, up to and including the material on conditional expectation. This refers to the material in the text and in the course notes, some of which are extensions of the text. Material prior to this test is also covered since the later topics build on earlier topics and ideas.

Nov 7, 2014 : LLN-CLT.pdf and two simulation examples LLN-CLT.R and options-eg2.R these ideas have to do with approximations used in statistics

Nov 10, 2014 : One section of Chapter 4 remains : it also has to do with approximations, but of a different nature than LLN and CLT. Momapprox.pdf

Nov 14, 2014 : Convergence-prob.pdf some details and the proof of the LLN and CLT, as well as the Poisson limit of rare Bernoulli (Poisson limit for Binomial distribution)

Nov 17, 2014 : RandSumsEgNov2014.pdf some remarks about random sums of random variables based on Question 2 from the November term test

Nov 19, 2014 : Chapter 6 deals with r.v.s that are used in the normal theory statistical inference NormalSampleMean-Variance.pdf

Nov 24, 2014 : term test 2 partial solutions Nov2014-partialSolution.pdf

I will treat Q3 (c) as a bonus question, so the grade is out of 46, and then rescaled to (50/46)*grade so it is out of 50

summary of test scores

Min. 1st Qu. Median Mean 3rd Qu. Max.

4 23 32 31 39 53

Nov 30, 2014 : The December 2013 exam Dec-2013.pdf

Formula sheet to go with the final exam formulae-for-final.pdf