Exam Coverage : Here is a outline of main
concepts and calculations that you should know.
Chap 2: Probability
- Sample space, simple events, compound events (union, intersection, and
complement), and Venn diagrams
- Probability, conditional probability and probability rules for compound events
- Independence and mutually exclusive
- Bayes theorem
- Basic counting rules (product rule, permutation, and combination)
Chap 3-4: Random Variables
- Probability distribution: pmf (discrete) and pdf (continuous)
- CDF, its use in calculating probabilities and its use in deriving density
functions
- How to calculate mean, variance (standard deviation), and expectation of
functions of random variables?
- Discrete r.v. : Binomial
- Continuous r.v. : Normal and exponential
- How to calculate percentiles and probabilities for any normal
distribution by using the normal table?
Chap 5:
- Equations (5.8) and (5.9) on page 244
Chap 6: Point Estimation
- Differences between point estimate and point estimator.
- Unbiased estimator. How to show an estimator is biased or unbiased?
- Likelihood function and maximum likelihood estimators (MLE). How
to derive MLE?
Chap 7.1-7.3: Confidence Intervals
- How to construct a confidence interval for population mean?
- How to interpret confidence intervals?
- Margin of error is the half width of a confidence
interval. How is the margin of error affected by sample size and
significant level?
- Given the margin of error, how to calculate the required sample size or the corresponding confidence level?
Chap 8.1-8.5: Hypothesis Testing
- Null and alternative hypotheses, rejection region, significant
level, and P-value.
- Type I and type II error. What is the relationship between type I
error and significant level?
- Test procedures for population mean for upper-tailed,
lower-tailed, and two-tailed tests, that is, you should know
how to determine the rejection regions or how to calculate P-values).
Chap 9.1, 9.3: Inferences Based on Two Samples
- Independent two-sample z-test
- Paired t-test
Chap 14.3: Goodness-of-Fit Test
- Chi-square test for two-way contingency table: what are the null
and the alternative? How to calculate the test statistic? How to determine
the degree of freedom?
Chap 12.1-12.3: Simple Linear Regression
- Simple linear regression model (normal error model).
- What is the principle of least squares?
- Fitted value, residual, and coefficient of determination.
- What is the distribution of beta_1? How to construct CI for
beta_1? How to do hypothesis testing on beta_1?