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Probability
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1
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C1
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Introduction, counting and sets
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1a: Introduction (PDF)
1b: Counting and Sets (PDF)
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Class 1 Slides (PDF)
Class 1 Slides with Solutions (PDF)
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Problem Set 1 (PDF)
Problem Set 1 Solutions (PDF)
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C2
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Probability basics
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2: Probability: Terminology and Examples (PDF)
R Tutorial 1A: Basics
R Tutorial 1B: Random Numbers
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Class 2 Slides (PDF)
Class 2 Slides with Solutions (PDF)
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S1
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Birthday matches; Introduction to R
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2
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C3
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Conditional probability, Bayes’ theorem
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3: Conditional Probability, Independence and Bayes’ Theorem (PDF)
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Class 3 Slides (PDF)
Class 3 Slides with Solutions (PDF)
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Problem Set 2 (PDF)
Problem Set 2 Solutions (PDF)
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C4
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Discrete random variables, expectation
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4a: Discrete Random Variables (PDF)
4b: Discrete Random Variables: Expected Value (PDF)
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Class 4 Slides (PDF)
Class 4 Slides with Solutions (PDF)
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S2
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Expectation; Simulation using R
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3
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C5
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Variance, continuous random variables
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5a: Variance of Discrete Random Variables (PDF)
5b: Continuous Random Variables (PDF)
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Class 5 Slides (PDF)
Class 5 Slides with Solutions (PDF)
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Problem Set 3 (PDF)
Problem Set 3 Solutions (PDF)
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S3
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Gallery of continuous variables, histograms
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5c: Gallery of Continuous Random Variables (PDF)
5d: Manipulating Continuous Random Variables (PDF)
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Class 5 Slides, cont’d (PDF)
Class 5 Slides, cont’d with Solutions (PDF)
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4
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C6
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Expectation, variance, law of large numbers and central limit theorem
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6a: Expectation, Variance and Standard Deviation for Continuous Random Variables (PDF)
6b: Central Limit Theorem and the Law of Large Numbers (PDF)
6c: Appendix (PDF)
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Class 6 Slides (PDF)
Class 6 Slides with Solutions (PDF)
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Problem Set 4 (PDF)
Problem Set 4 Solutions (PDF)
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C7
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Joint distributions: independence, covariance and correlation
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7a: Joint Distributions, Independence (PDF)
7b: Covariance and Correlation (PDF)
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Class 7 Slides (PDF)
Class 7 Slides with Solutions (PDF)
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S4
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Covariance, correlation, CLT
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5
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C8
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Review for exam 1
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Class 8: Exam Review (PDF)
Class 8: Exam Review Solutions (PDF)
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Class 8 Slides (PDF)
Class 8 Slides with Solutions (PDF)
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C9
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Exam 1
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Statistics: Bayesian Inference
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5
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C10
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Introduction to statistics; maximum likelihood estimates
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10a: Introduction to Statistics (PDF)
10b: Maximum Likelihood Estimates (PDF)
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Class 10 Slides (PDF)
Class 10 Slides with Solutions (PDF)
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6
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C11
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Bayesian updating with known discrete priors
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11: Bayesian Updating with Discrete Priors (PDF)
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Class 11 Slides (PDF)
Class 11 Slides with Solutions (PDF)
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Problem Set 5 (PDF)
Problem Set 5 Solutions (PDF)
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C12
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Bayesian updating: probabilistic prediction; odds
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12a: Bayesian Updating: Probabilistic Prediction (PDF)
12b: Bayesian Updating: Odds (PDF)
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Class 12 Slides (PDF)
Class 12 Slides with Solutions (PDF)
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S5
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Bayesian updating
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7
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C13
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Bayesian updating: continuous prior, discrete data
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13a: Bayesian Updating with Continuous Priors (PDF)
13b: Notational Conventions (PDF)
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Class 13 Slides (PDF)
Class 13 Slides with Solutions (PDF)
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C14
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Beta distributions: continuous data
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14a: Beta Distributions (PDF)
14b: Continuous Data with continuous Priors (PDF)
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Class 14 Slides (PDF)
Class 14 Slides with Solutions (PDF)
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S6
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Continuous data, continuous priors
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8
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C15
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Conjugate priors; choosing priors
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15a: Conjugate Priors: Beta and Normal (PDF)
15b: Choosing Priors (PDF)
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Class 15 Slides (PDF)
Class 15 Slides with Solutions (PDF)
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Problem Set 6 (PDF)
Problem Set 6 Solutions (PDF)
Problem Set 6 R Code (R)
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C16
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Probability intervals
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16: Probability Intervals (PDF)
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Class 16 Slides (PDF)
Class 16 Slides with Solutions (PDF)
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S7
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No studio
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Statistics: Frequentist Inference—Null Hypothesis Significance Testing (NHST)
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9
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C17
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Frequentist methods; NHST
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17a: The Frequentist School of Statistics (PDF)
17b: Null Hypothesis Significance Testing I (PDF)
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Class 17 Slides (PDF)
Class 17 Slides with Solutions (PDF)
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Problem Set 7 (PDF)
Problem Set 7 Solutions (PDF)
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C18
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NHST II: Significance level, power, t-tests
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18: Null Hypothesis Significance Testing II (PDF)
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Class 18 Slides (PDF)
Class 18 Slides with Solutions (PDF)
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S8
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Rejection regions; NHST
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10
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C19
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NHST III: Gallery of tests
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19: Null Hypothesis Significance Testing III (PDF)
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Class 19 Slides (PDF)
Class 19 Slides with Solutions (PDF)
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Problem Set 8 (PDF)
Problem Set 8 Solutions (PDF)
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C20
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Comparison of Bayesian and frequentist inference
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20: Comparison of Frequentist and Bayesian Inference (PDF)
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Class 20 Slides (PDF)
Class 20 Slides with Solutions (PDF)
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S9
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NHST; comparing frequentist and Bayesian methods
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11
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C21
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Review for exam 2
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Class 21 Slides (PDF)
Class 21 Solutions File (PDF)
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S10
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Exam 2
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Statistics: Confidence Intervals; Regression
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12
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C22
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Confidence intervals for normal data
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22: Confidence Intervals Based on Normal Data (PDF)
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Class 22 Slides (PDF)
Class 22 Slides with Solutions (PDF)
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Problem Set 9 (PDF)
Problem Set 9 Solutions (PDF)
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C23
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Confidence intervals II
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23a: Confidence Intervals: Three Views (PDF)
23b: Confidence Intervals for the Mean of Non-normal Data (PDF)
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Class 23 Slides (PDF)
Class 23 Slides with Solutions (PDF)
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S11
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Confidence intervals III
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13
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C24
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Bootstrap confidence intervals
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24: Bootstrap Confidence Intervals (PDF)
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Class 24 Slides (PDF)
Class 24 Slides with Solutions (PDF)
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C25
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Linear regression
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25: Linear Regression (PDF)
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Class 25 Slides (PDF)
Class 25 Slides with Solutions (PDF)
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S12
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Bootstrapping; linear regression
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14
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C26
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Review for final exam
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Class 26 Slides (PDF)
Class 26 Problems File (PDF)
Class 26 Solutions File (PDF)
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C27
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Review for final exam, cont’d
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Class 27 Slides (PDF)
Class 27 Problems File (PDF)
Class 27 Solutions File (PDF)
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15
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Final exam
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