October 7, 2007

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### What's on the Exam? #1

The best study guides are the homework sets, including the solution sheets. Also, the problems in the text are good practice.

The exam covers these parts of the text:

• Section 2.2. Also, notion of a partition of S; i.e., a (finite or countably infinite) collection of sets C1, C2, ... that are pairwise disjoint and whose union is S.
• Section 2.3.
• Section 2.4, not including the Case Studies 2.4.1, 2.4.2, 2.4.3. Emphasis on multiplication rule and "Law of Total Probability." Also, Bayesian updates for computing P(C1|B),...,P(Cn|B).
• Section 2.5.
• Section 2.6, and, with less emphasis, the gist of 2.7.
• Section 3.2 through p. 118 (skip hypergeometric distributions)
• Section 3.3. Emphasize general role of cdf; use term pmf in place of pdf (for discrete distributions); skip Benford.
• Section 3.4. Emphasize role of cdf; also emphasize transformations (p. 171)
• Section 3.5. Note Lazy Statistician's Rule (pp. 186-187). Note also E(aX+b)=aE(X)+b.
• Section 3.6. Var(X) = E((X-mu)squared) = E(X2)-(E(X))2; Var(aX+b)=a2 Var(X); std. dev. of aX = |a| times std. dev. of X. Emphasize higher moments (p. 199) even though we mostly just have a definition.
• Section 3.7 through p. 206; also, p. 211.

Also, we considered some specific distributions. It would be good to be comfortable with these, but it is not necessary to memorize formulas for now, even the definitions of the distributions, since these will be given in the exam when needed.

• Discrete distributions:
• uniform on a finite set of values
• Bernoulli (=binary, indicator, dummy) with parameter p
• binomial with parameters n, p
• geometric with mean mu
• Poisson with mean mu
• Continuous distributions:
• Uniform on interval [a, b]
• Exponential with mean mu
• Standard normal
• normal with mean mu, standard deviation sigma
• gamma with parameters a, b

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