Statistical Computing Homework #7

  1. Modify the code provided in horton-tas to illustrate at least two characteristics of the Central Limit Theorem.
  2. Modify the code provided in horton-tas to simulate observations from a bivariate normal distribution with moderate negative association. Make one additional change to simulate observations from a bivariate normal distribution with strong negative association.
  3. Provide an example that illustrates how to obtain the power of a test. You may use simulation to approximate the power of the test in a particular situation.
  4. Suppose X follows a uniform distribution on the interval from 10 to 20. Use numerical integration to find E(X), E(X^2), and Var(X). Compare your approximate answers with the exact values. Are you happy with the accuracy of your approximations? Comment.