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Data 88S Textbook
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Chapters
1. The Basics
1.1. Probabilities as Proportions
1.2. Exact Calculation, or Bound?
1.3. Fundamental Rules
1.4. Exercises
2. Intersections and Conditioning
2.1. The Chance of an Intersection
2.2. Symmetry in Simple Random Sampling
2.3. Bayes’ Rule
2.4. Use and Interpretation
2.5. Independence
2.6. Exercises
3. Random Counts
3.1. Success and Failure
3.2. Random Variables
3.3. The Binomial Distribution
3.4. The Hypergeometric Distribution
3.5. Examples
3.6. Exercises
4. Infinitely Many Values
4.1. Cumulative Distribution Function (CDF)
4.2. Waiting Times
4.3. Exponential Approximations
4.4. The Poisson Distribution
4.5. Exercises
5. Expectation
5.1. Definition
5.2. Functions of Random Variables
5.3. Method of Indicators
5.4. Unbiased Estimators
5.5. Conditional Expectation
5.6. Expectation by Conditioning
5.7. Exercises
6. Measuring Variability
6.1. Variance and Standard Deviation
6.2. Simplifying the Calculation
6.3. Markov’s Inequality
6.4. Chebyshev’s Inequality
6.5. Exercises
7. The Variance of a Sum
7.1. Sums of Independent Random Variables
7.2. Sampling Without Replacement
7.3. The Law of Averages
7.4. Exercises
8. Central Limit Theorem
8.1. The Distribution of a Sample Sum
8.2. Standard Normal Curve
8.3. Normal Approximation
8.4. How Large is “Large”?
8.5. Exercises
9. Inference
9.1. Confidence Intervals: Method
9.2. Confidence Intervals: Interpretation
9.3. Testing Hypotheses
9.4. A/B Testing: Fisher’s Exact Test
9.5. Exercises
10. Probability Density
10.1. Density
10.2. Expectation and Variance
10.3. Exponential Distribution
10.4. The Normal Distribution
10.5. Exercises
11. Bias, Variance, and Least Squares
11.1. Bias and Variance
11.2. Examples
11.3. Least Squares Linear Regression
11.4. Bounds on Correlation
11.5. The Error in Regression
11.6. Exercises
12. Inference in Regression
12.1. The Simple Linear Regression Model
12.2. The Distribution of the Estimated Slope
12.3. Towards Multiple Regression
12.4. Exercises
Index
