Midterm Topics

midterm in class, Monday, July 21

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You will be allowed one two-sided page of notes. Calculators will be allowed, although only simple computations will be necessary. Here is a list of topics that could be covered on the midterm, with suggested exercises (some of which are considerably harder than the midterm will be). Note that some suggested exercises were on the homework.

  • Chapter 1:
    • Probability distributions: definition, events and set notation, rules, Bayes' rule, odds functions.
    • the Birthday problem.
    • suggested exercises: 1.R: 11, 13, 16, 18; 2.R: 14, 23.
  • Chapter 2:
    • Binomial distribution: definition, properties, square root law, law of large numbers, Gaussian approximation, Poisson approximation.
    • Gaussian curve and CDF.
    • Hypergeometric distribution: definition.
    • log(1+x) approximation.
    • suggested exercises: 2.5: 3, 7; 2.R: 13, 20, 22, 34; 3.1: 13; 3.R: 11, 20 .
  • Chapter 3:
    • Random variables: joint and marginal distributions, equality in distribution, conditional distributions, independence, multiplication rule.
    • Multinomial distribution: definition, conditional distribution.
    • Expectation: definition, linearity/additivity, as a long run average, tail sum formula, indicators.
    • Minimizing mean square error.
    • Standard deviation (SD) and Variance: definition and computation, additivity, scaling.
    • Central Limit Theorem: standardization, Chebyshev's inequality, square root law, law of averages, random walk example.
    • Geometric distribution: definition, properties
    • Negative binomial distribution
    • Collector's problem
    • Poisson distribution: defintion.
    • suggested exercises: 3.1: 16, 20, 21; 3.2: 13, 15, 22 (use the shifting method to evaluate the sums); 3.3: 25, 30; 3.5: 1, 2; 3.4: 6, 15; 3.R: 4, 10, 21, 30 (a,b); p.491: 1.

Omitted topics: topics from chapters 1-3 in the book that we've skipped or haven't gotten to yet.

  • 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.
  • Section 2.5: properties of Poisson distribution -- we'll do this, but it won't be on the midterm.
  • All of Section 3.6: Symmetry.