Lectures: Monday, Wednesday, and Friday, 10:00-11:00, Biostat Conference Room
Lab: Friday 11:00-12:00, Biostat Conference Room
Office hours:
Date | Lecture | Topic | Reading | Homework | Due at Start of Class | |||||
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Aug 23 | 1 | Introduction and Set Theory | CB 1.1 | |||||||
Aug 25 | 2 | Axiomatic Foundations / Calculus of Probabilities | 1.2 | Homework for Lectures 1-2 | ||||||
Aug 25 | Lab 1 | Poker Probabilities ( poker-draw.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 1-4 | ||||||||
Sept 1 | Lab 2 | Birthday problem ( b-day.R) | ||||||||
Sept 4 | LABOR DAY | |||||||||
Sept 6 | 5 | Random Variables /Distribution Functions | 1.4-1.5 | |||||||
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 5-7 | ||||||||
Sept 15 | Lab 4 | Distributions and Transformations ( distributions-transformations.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 non-negative continuous random variable with CDF F(x) and E(X)< infinite. Show that E(X)=integral from 0 to infinity (1-F(x))dx. | ||||||
Sept 20 | 10 | Discrete Distributions | 3.1-3.2 | 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 8-9, and Lab 4. |
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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 |
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Sept 29 | Lab 6 | Review and Discuss Exam | ||||||||
Oct 2 | 12 | Exponential Families / Location and Scale Families | 3.4-3.5 | 3.28 (for a-c 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 11-12 | |||||||
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 | |
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Oct 13 | FALL BREAK | |
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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, 4.45a-b, 4.58a-b | ||||||
Oct 20 | Review and Discuss Homework Problems | HW for lectures 13-16 | ||||||||
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). |
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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 17-19 | ||||||||
Oct 27 | Lab 9 | Review for EXAM ( 2011 exam with solutions, 2014 exam , solutions-a, solutions-b, solutions-c) | ||||||||
Oct 30 | EXAM | |||||||||
Nov 1 | 20 | Random Samples and Sums of Random Variables | 5.1-5.2 | 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(X1-Xbar,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 20-21 |
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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 22-23 |
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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(1-p2)/(p2(1-p1)))? | ||||||
Dec 1 | Review and Discuss Homework Problems |
HW for lectures 24-25, and Lab 12 |
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Dec 1 | Lab 13 | Approaches for generating a random sample | 5.6 | accept-reject.R: Code to generate from Beta(2,2) distribution with Unif(0,1) ; accept-reject-beta.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 |
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Dec 11, 12-3 | FINAL EXAM | 2015 Exam and Solutions, 2014 Exam and Solutions, 2016 Exam and Solutions |