Review for Midterm 2

• Time and Places of Exam : In class, from 1:15pm to 2:30pm on Thursday, Nov 11 2004
  
  
• Exam Materials : The exam is closed book. You can prepare a formula sheet: a single 8x11 sheet on which you can write whatever you like. Standard normal CDF, critical values for student t, and a two-page formula sheet (like this) are attached to the exam. You should bring a calculator.
  
  
• Exam Coverage : Here is a outline of main concepts and calculations that you should know.
  

  Chap 5.1, 5.2: Joint Distributions

  • Joint, marginal, and conditional probability mass functions; joint, marginal, and conditional density functions; independence.
  • Given the joint distribution, how to calculate the marginals and how to determine whether two random variables are independent or not?
  • Given the joint distribution, how to calculate the conditional distributions, conditional expectations, and conditional probabilities?
  • Expectation, covariance, correlation coefficient and related calculations. How to inteprete correlation coefficient? How are covariance and correlation affected by a linear transformation of the random variables?

  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 and proportion?
  • 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?
  • Predictive intervals.

  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? How to calculate the type II error?
  • Test procedures for population mean.
  • How to determine the rejection regions (or how to calculate P-values) for upper-tailed, lower-tailed, and two-tailed tests?

  Everyone has their own approaches to study, but here are some (unsolicited) advice:
  (1) Go through the outline of concepts above and make sure you understand them all;
  (2) Go over the lecture notes, homework assignments, and textbook examples.