Topics for Exam Review: Complete List, with associated numbered 
sections of the book, is given on the course web-page under 
"15-week Course coverage based on Devore Book and 38 classes" 
and under "Course Outline". A quick summary of book sections for
which you are resonsible on the exam, is:

1.1-1.4 (only material on sample mean, variance ,quantiles, 
and scaled relative frequency histograms); 2-1-2.5, 3.1-3.6 (omitting
material on negative binomial in 3.5 and on Poisson process in 3.6);
4.1-4.5 (only the exponential, not Gamma, in 4.4); Handout material on
Transformation and Simulation 5.1-5.3 (discrete case only), 5.4-5.5; 
6.1, 6.2 (Moment estimator only); 7.1-7.3; 8.1-8.2. 

A briefer list of topics and problem types which you have seen 
and are responsible for on the exam, is the following:

Chapter 1:
(1) Definition of empirical distribution function, sample mean 
and sample quantiles, and construction of scaled relative 
frequency histograms.

Chapter 2:
(2) Probability axioms, construction of sample spaces, expression 
of events as unions and intersections, combinatorial and counting 
techniques (with numerators of expressions usually given by the 
multiplication principle as products of binomial coefficients).

(3) Conditional probability and Bayes Theorem, and use of 
independence and given conditional probabilities to get 
probabilities of intersections. Probability that event A occurs 
before event B in repeated independent trials.

Chapters 3 and 4:
(4) Sampling with and without replacement from urns, binomial 
and hypergeometric probability distributions.

(5) Random variables, probability mass functions in discrete 
case and density functions in continuous case. Calculations of 
probabilities of varables falling in intervals of values, of 
distribution functions, of means and variances and expectations 
of other functions of random variables (moments, etc.). Standard
formulas for densities, means, variances, distribution functions 
for the main examples of discrete r.v.'s (binomial, Poisson, 
hypergeometric, geometric) and continuous r.v.'s (Uniform, 
Exponential, Normal, Lognormal). Calculation of sample quantiles
(median, upper quartile, etc.) of continuous r.v. by inverting d.f.

(6) Binomial approximation to hypergeometric (equivalence of 
with- and without-replacement sampling when population size N is 
large, and sample-size n and proportion D/N=p remain fixed), 
Poisson approximation to Binomial distribution (large n, moderate 
np), and Normal approximation to Binomial (large n, fixed p).

EXTRA MATERIALS FROM HANDOUTS
(7) Change of variable: distribution function and density of r.v.
Y=g(X) defined in terms of r.v. X with known density, with g a 
known invertible differentiable function.

(8) Simulation: how to define a continuous r.v. X with specified 
d.f. F as a function g(U) where U ~ Uniform[0,1] (and g is inverse 
of d.f. F). Interpretation of probability of [a<X<b] as the 
relative frequency over many independently generated values X_1, 
..., X_n of  the occurence of [a<X_i<b]. Interpretation of E(X) 
or E(h(X)) as large-sample averages  (X_1+...+X_n)/n or (h(X_1)+
...+h(X_n))/n  respectively (Law of Large Numbers).

Chapter 5: 
(9) Joint probability mass function for 2 discrete r.v.'s. Marginal
probability mass functions, checking for independence, calculation 
of covariance and correlation. Means and variances of sums of 
(weighted) sums of independent random variables.

(10) General definition of independent events and random variables.
Law of Large Numbers and Central Limit Theorem. Approximate 
calculation of probabilities for averages Xbar or sums X_1+...+X_n
to lie in specified intervals (a,b) via normal distribution. Exact 
normal distribution for (weighted) sums of independent normal r.v.'s

Chapter 6:
(11) Notion of unknown parameter of a probability distribution for 
data. Definition of statistic, estimator, consistent and unbiased 
estimators. Method of moments (estimating a parameter by finding 
what function it is of the mean, and estimating the latter by Xbar).

Chapter 7:
(12) Confidence intervals with specified confidence level 1-alpha 
for the sample mean, one and two-sided, small (normal-data) and 
large sample, with known and unknown variance. Normal and t 
distribution percentage points. Prediction intervals, and sample size
needed to achieve confidence interval of specified width.

Chapter 8:
(13) Hypothesis testing, definitions. Calculation of size 
(= significance level = type I error probability) and power in 
simple examples. Expression rejection regions, in testing the null 
hypothesis of a specified mean against one- and two- sided 
alternatives, in terms of (failure of null-hypthesis parameter to 
fall in) the corresponding confidence interval. Formula for power 
function of one-sided hypothesis test for normal mean, and 
sample-size needed to achieve specific alpha, beta for specific 
null-hypothesis and alternative-mean.