In-Class Final Topics

You will be allowed three two-sided pages of notes. Calculators will be allowed, although only simple computations will be necessary. The final will mostly cover material since the midterm (chapters 4-6), and will focus more on computation (rather than interpretation) and on topics not emphasized by the takehome final. (suggested problems are in parentheses -- note that some were on the homework)

• Chapters 1-3: (see midterm notes for more detail -- these are "selected topics")
• Probability distributions: events and set notation, rules.
• Binomial distribution: definition, properties, square root law, law of large numbers, Gaussian approximation, Poisson approximation.
• log(1+x) approximation.
• Random variables: joint and marginal distributions, conditional distributions, independence, multiplication rule.
• Expectation: definition, linearity/additivity, tail sum formula, indicators.
• Standard deviation (SD) and Variance: definition and computation, additivity, scaling.
• Central Limit Theorem: standardization, square root law, law of averages, random walk example.
• Geometric distribution: definition, properties
• First Fish principle a.k.a. craps principle. (3.4: #5, 11)
• Chapter 4:
• Probability densities: definition, properties, and use.
• Exponential distribution: definition, memorylessness, CDF.
• Poisson process/scatter: definition, Poisson counts, Exponential waiting times, independence of disjoint sets.
• Gamma distribution: definition, sums of exponentials.
• Change of Variable: how to do it. (4.4 #4,5)
• Cumulative Distribution Functions: definition, use for simulation. (4.5: #5)
• Order statistics: derivation of general formula, Beta distribution. (4.6: #3)
• Chapter 5:
• Joint densitites: definition, properties, and use.
• Uniform distribution on a geometric area. (5.1: #4)
• Independent Normals: linear combinations and rotations; Rayleigh distribution. (5.3: #3)
• Chapter 6: (in order from class; not from the book)
• Covariance and Correlation: definition, computation, properties, bilinearity of covariance. (6.4: #8, 9)
• Bivariate (correlated) Normals: definition, correlation, uncorrelated = independent, conditioned. (6.5: #3, 4)
• Conditional distributions. (6.2: #2,3,11)
• Conditional expectation: computation.
• Conditional densities: computation.

Omitted topics: topics in the book that we've skipped.

• Anything about skewness or skew-normal approximation.
• All of Section 1.2: Interpretations
• In Section 2.2: Markov's inequality
• Much of Section 2.3: derivation of Gaussian approx.
• In Section 3.2: other loss functions.
• All of Section 3.6: Symmetry.
• In Section 4.1: integral approx. for averages.
• In Section 4.2: Gamma distribution for non-integer shape.
• All of Section 4.3: Hazard rates.
• In Section 4.6: Beta distribution for non-integer parameters.
• In Section 5.3: Chi-Squared distribution.
• All of Section 5.4: Operations.
• Sections 6.2-6.3: many of the properties of conditional expectation.
• Section 6.4: Correlation and Conditioning.
• Section 6.5: Independence of linear combinations.