COURSE COVERAGE
Date  Coverage  Homework (from text, 3rd edition) 

Jan.4  Introduction. Review of RVs: cdf, pdf, pmf.  You can read chapter 1 and 2 of the text for review. 
Jan.6  Review continued: examples of different continuous and discrete random variables.  Chapter 1: 1, 4, 7 (also sketch), 14, 35, 38, 40, 49. Also this. (N.B. all except #49 should be review.) 
Jan.9  Transformations of random variables (review).  Chapter 2: 21, 44, 56, 60, 61, 68 
Jan.11  Transformations of random variables con't. 

Jan.13  Transformations of random variables  generating an RV starting from the
Uniform[0,1]
R script 

Jan.16 
Bivariate pmf and marginals.
QUIZ 
Chapter 3: 1a, 2 
Jan.18  Bivariate pdf and marginals.
Quiz returned 

Jan.20  Finding marginals (con't), bivariate normal, independence.
R script 
Chapter 3: 12ab, 14a, 15abcd, 17ab, 18abc 
Jan.23  Copulas, conditional distributions, law of total probability. 

Jan.25  Conditional probability: more examples. Introduction to bivariate transformations. 

Jan.27  Continuation of bivariate transformations: sums and ratios. 

Jan.30  General formula for bivariate transformations  Chapter 3: 51, 55, 56, 58, 61, 62, 63a, 64 
Feb.1  Linear transformations of normal are normal. Order statistics: min and max.  STUDY! I'll post stuff from this material later. 
Feb.3  TEST ONE  
Feb.6  Another normal example. Continuation of order statistics. 

Feb.8  One last example from order statistics. Started on expectations  Chapter 4 of text.  Chapter 4: 2, 4, 7, 14 
Feb.10  Continued with expectations (mainly review from 2030). Test one was returned.  Chapter 4: 13 (try integration by parts, but there's a better way to do it), 16, 17 
Feb.13  Properties of expectations, variance, covariance. 

Feb.15  Conditional expectation & prediction, law of total expectation.  Chapter 4: 61abc, 62, 63, 66, 77 
Feb.17  Conditional expectation con't. 

Feb.2025  READING WEEK  
Feb.27  Review.  STUDY! 
Feb.29  More review.  STUDY! (please) 
March 2  TEST TWO  
March 5  Random sums and conditional variance. Started on moment generating functions. Test two was returned. 

March 7  Moment generating functions. 

March 9  Law of large numbers and convergence in probability. Simulations in R. 

March 12  Central limit theorem and convergence in distribution. Simulations in R. 

March 14  One more CLT example and Section 6.2 of the text. 

March 16  Section 6.3 of the text. Estimation example.  Chapter 6:7,8. Read proof of Theorem A on page 195196 in the text. How is it different than what we did in class? What techniques does it use? What techniques did we use? 
March 19  Finished Section 6.3. Motivated discussion of ztest and ttest. 

March 21  The ztest: significance level, pvalue, rejection region, evaluating results, type I and II error, power. Most of this should be review, except maybe the idea of power.  You may need to look back to your 1131 work for a quick review. Also, this (you may not be able to answer the power questions until after Friday's lecture). 
March 23  Power: R script 

March 26  One and twosample ttest (MATH 1131 review and Section 11.2 of text) 

March 28  One way ANOVA (Section 12.2 of text)  Chapter 12: 2,3,6,21 
March 30  TEST THREE  
April 2  One way ANOVA con't. 
