Exam Coverage
Chap 2: Probability
- Probability, conditional probability,
and probability rules for compound events (union, intersection, and complement).
- Counting rules (product rule, permutation, and combination)
- Pairwise independent events may NOT be mutually independent.
- How to calculate he probability for independent events and
mutually exclusive (or disjoint) events? What is the difference
between these two concepts?
- Bayes theorem.
Chap 3.1-3.4: Discrete Random Variables
- Probability mass function (pmf). Important property: sum of pmf
is equal to 1.
- Mean, variance (standard deviation), and expectations of function
of random variables.
- Rules of expected values (p115) and rules of variance (p118).
- Required distributions: Binomial.
Chap 4.1-4.3 and pp 177-178: Continuous Random Variables
- pdf and CDF; How to derive pdf using CDF method?
- Mean, variance (standard deviation), and expectations of
functions of random variables.
- Rules of expectation and variance.
- Required distributions: Normal, Uniform, and Exponential.
- Exclude (1) normal
approximation to binomial distribution and
continuity correction (pp 169-170); (2) connection between exponential
and Poisson.
Chap 5.1-5.2, 5.4-5.5: Joint Distributed Random Variables
- Joint and marginal pdf.
- How to calculate probabilities when the integration areas (or
their complements) are triangles?
- Independence.
- Given the joint distribution, how to calculate the marginals and how to determine whether two random variables are independent or not?
- Covariance, correlation coefficient and related calculations. How
to interpret correlation coefficient? How are covariance and
correlation affected by a linear transformation of the random
variables?
- Central Limit Theorem (CLT).
- Exclude pp
213-215.
Chap 6.1: Point Estimation
- Differences between point estimator (a random variable) and point
estimate (a number calculated from a sample).
- Unbiased estimators. How to show an estimator is biased or unbiased?
- How to calculate the variance (or standard deviation) of an estimator?
- How to derive MLE? How to use the invariance principle to derive
MLE for functions of parameters?
- Exclude
(1) estimators with minimum variance (pp 260-261); (2) bootstrap
(pp264-265).
Chap 7.1-7.3: Confidence Intervals (CI)
- CI for a population mean and proportion. For CIs for population proportion, use eq (7.11) instead of
(7.10).
- CI for a linear combination of population
means.
- Interpretation of a CI.
- Relationship between the width of a CI and the sample size and the
significant level.
- Given the width of CI, how to calculate the required sample size
or the corresponding confidence level?
- Exclude (1) one-sided CIs; (2) prediction
intervals; (3) tolerance intervals.
Chap 8.1-8.4: Hypotheses Testing
- Null and alternative hypotheses, rejection region, significant level, and P-value.
- Type I and type II errors. What is the relationship between type I
error and significant level? How to calculate type II error for
one-sided and two-sided test?
- Test procedures for population mean and proportion.
- How to determine the rejection regions (or how to calculate
P-values) for upper-tailed, lower-tailed, and two-tailed tests?
- Connection between two-tailed tests and confidence intervals.
- Exclude (1)
sample size determination (based on type II error) type of
calculation; (2) small-sample test for population proportion on pp
342; (3) chap 8.5.
Chap 9.1-9.4: Inference Based on Two Samples
- z-test (for population mean and proportion) and CI for independent two samples with large sample
size.
- Pooled t-test and CI for independent two samples with equal
variance.
- Paired t-test and CI.
- Exclude (1) pp
364-366; (2) two sample t-test with unequal variance; (3) Type II
error and sample sizes.
Chap 14.1, 14.3: Goodness-of-fit tests
- Chi-squared tests for one-way tables.
- Chi-squared tests for two-way tables.
- Exclude (1) pp
639-640; (2) chap 14.2;