Lectures: Monday, Wednesday, and Friday, 10:0011:00, Biostat Conference Room
Lab: Friday 11:0012:00, Biostat Conference Room
Office hours:
Date  Lecture  Topic  Reading  Homework  Due at Start of Class  

Aug 23  1  Introduction and Set Theory  CB 1.1  
Aug 25  2  Axiomatic Foundations / Calculus of Probabilities  1.2  Homework for Lectures 12  
Aug 25  Lab 1  Poker Probabilities ( pokerdraw.R)  
Aug 28  3  Counting / Enumerating Outcomes  1.2  1.16, 1.17, 1.18, 1.20, 1.22  
Aug 30  4  Conditional Probability and Independence  1.3  1.33, 1.34, 1.36, 1.37b, 1.38, 1.39, 1.40  
Sept 1  Review and Discuss Homework problems  HW for lectures 14  
Sept 1  Lab 2  Birthday problem ( bday.R)  
Sept 4  LABOR DAY  
Sept 6  5  Random Variables /Distribution Functions  1.41.5  
Sept 8  6  Density and Mass Functions  1.6  1.49, 1.50, 1.51, 1.53, 1.54, 1.55  
Sept 8  Lab 3  Delirium Study, Conditional Probability, and Causal inference; delirium.pdf  
Sept 11  7  Distributions of Functions of a Random Variable  2.1  2.1, 2.2, 2.3, 2.4, 2.6 (don't need to show pdf integrates to 1), 2.8 (don't need to show it's a cdf)  
Sept 13  8  Expected Values  2.2  
Sept 15  Review and Discuss Homework Problems  HW for lectures 57  
Sept 15  Lab 4  Distributions and Transformations ( distributionstransformations.R)  Generate 1000 X from GAM(3,2) distribution. Compare empirical density and cdf with true density and cdf. Generate Y=UNIF(0,1) using probability integral transformation and verify that empirical cdf is similar to true cdf. Next, generate 1000 U from UNIF(0,1) and then generate V~GAM(3,2) using the inverse cdf of a gamma distribution. Please turn in plots of your simulations as well as printout of your code.  
Sept 18  9  Moments and Moment Generating Functions  2.3  2.15, 2.20, 2.24, 2.33. EXTRA: Let X be a nonnegative continuous random variable with CDF F(x) and E(X)< infinite. Show that E(X)=integral from 0 to infinity (1F(x))dx.  
Sept 20  10  Discrete Distributions  3.13.2  3.1, 3.2, 3.3, 3.4, 3.5 (probably need to use R), 3.7, 3.8  
Sept 22  Review and Discuss Homework Problems  HW for lectures 89, and Lab 4. 

Sept 22  Lab 5  Review for Exam ( 2011 Exam and Solutions, 2014 exam, 2014 solutions)  
Sept 25  EXAM  
Sept 27  11  Continuous Distributions  3.3  3.17, 3.22d, 3.23, 3.24a (hint: substitute z=y^gamma/beta),3.24c (hint: substitute z=1/y), 3.25, 3.26  
Sept 29  Review and Discuss Homework Problems  HW for lecture 10 

Sept 29  Lab 6  Review and Discuss Exam  
Oct 2  12  Exponential Families / Location and Scale Families  3.43.5  3.28 (for ac do it only for both unknown), 3.29, 3.30 (some versions of the book have part b for the beta distribution don't do this; part b should be for a Poisson distribution), 3.37, 3.42  
Oct 4  13  Joint and Marginal Distributions  4.1  4.1, 4.1d: P( abs(X+Y) <1), 4.4, 4.5  
Oct 6  14  Review and Discuss Homework Problems  HW for lecture 1112  
Oct 6  Lab 7  Survival Analysis (Exponential Distributions and Censoring)  
Oct 9  14  Conditional Distributions and Independence  4.2  4.7, 4.9, 4.10, 4.11, 4.12, 4.13  
Oct 11  15  Bivariate Transformations [BRYAN OUT] 
4.3  4.15, 4.16, 4.19, 4.20, 4.22  

Oct 13  FALL BREAK  

Oct 16  16  Hierarchical Models and Mixture Distributions [BRYAN OUT] 
4.4  4.31, 4.32a, 4.34a, 4.35  
Oct 18  17  Covariance and Correlation  4.5  4.41, 4.42, 4.43, 4.45ab, 4.58ab  
Oct 20  Review and Discuss Homework Problems  HW for lectures 1316  
Oct 20  Lab 8  
Oct 23  18  Multivariate Distributions  4.6  4.36, 4.39 (hint for Cov(X1+X2): find Var(X1+X2)), Using pdf in Example 4.6.1, find a) f(x1,x2,x3), b) f(x4 given x1,x2,x3), c) P(X1<1/2,X2<1/2,X3<1/2), d) P(X4<1/2 given X1=X2=X3=1/2). 

Oct 25  19  Inequalities and Identities  3.6 and 4.7  3.46, 4.63  
Oct 27  Review and Discuss Homework Problems 
HW for lectures 1719  
Oct 27  Lab 9  Review for EXAM ( 2011 exam with solutions, 2014 exam , solutionsa, solutionsb, solutionsc)  
Oct 30  EXAM  
Nov 1  20  Random Samples and Sums of Random Variables  5.15.2  5.1, 5.3, 5.5, 5.8a, c (assume E(X)=0 and use part a)  
Nov 3  Review and Discuss EXAM  
Nov 3  Lab 10  Ordinal Residual  
Nov 6  21  Normal Distribution (Properties of Sample Mean and Variance)  5.3  5.10 (use Stein's lemma for a), 5.11, 5.15, Additional Problem: Xi ~ iid N(mu, sigma^2). a) show that Cov(X1Xbar,Xbar)=0; b) use (a) to show that xbar is independent of S^2.  
Nov 8  22  Normal Distribution (Derived Distributions)  5.3  5.17, 5.18a,b,c (use version of Sterling's formula given in 5.35b)  
Nov 10  Review and Discuss Homework Problems  HW for lectures 2021 

Nov 11  Lab 11  Approaches for generating a random sample  5.6  
Nov 13  23  Order Statistics  5.4  5.21, 5.22, 5.24, 5.27  
Nov 15  24  Convergence Concepts (convergence in probability, a.s., distribution)  5.5  5.32, 5.42  
Nov 17  Review and Discuss Homework Problems 
HW for lectures 2223 

Nov 17  Lab 12  Approaches for generating a random sample R code  5.6  
Nov 20  THANKSGIVING  
Nov 22  THANKSGIVING  
Nov 24  THANKSGIVING  
Nov 27  25  Convergence Concepts (central limit theorem)  5.5  5.29, 5.30, 5.31, 5.34, 5.35  
Nov 29  26  Convergence Concepts (delta method)  5.5  5.44. Additional problem: Let Xi ~ iid BIN(1,p1), Yi ~ iid BIN(1,p2), i=1,...n for both, all Yi independent of Xi; What is the limiting distribution of the sample log odds ratio (logOR) where logOR=log(p1(1p2)/(p2(1p1)))?  
Dec 1  Review and Discuss Homework Problems 
HW for lectures 2425, and Lab 12 

Dec 1  Lab 13  Approaches for generating a random sample  5.6  acceptreject.R: Code to generate from Beta(2,2) distribution with Unif(0,1) ; acceptrejectbeta.R: Code to generate from Beta(6.1,1.8) distribution with Unif(0,1)  
Dec 4  27  Review and Discuss Homework Problems

Code generating from biased Weibull distribution  HW for lecture 26 and labs 13  
Dec 6  Review for FINAL EXAM


Dec 11, 123  FINAL EXAM  2015 Exam and Solutions, 2014 Exam and Solutions, 2016 Exam and Solutions 