Exercises

Assigned Problems are in bold and others are for Class discussion

  1. HMC Section 4.1 p. 201: 4.1.1, 4.1.7, 4.1.10, 4.1.24, 4.1.25
  2. HMC Section 4.2 p. 207: 4.2.2, 4.2.4
  3. HMC Section 4.3 p. 218: 4.3.4, 4.3.7, 4.3.10, 4.3.19
  4. HMC Section 4.4 p. 225: 4.4.9, 4.4.10
  5. HMC Section 4.5 p. 230: 4.5.1, 4.5.2
  6. HMC Section 5.1 p. 238: 5.1.6
  7. HMC Section 5.2 p. 246: 5.2.1, 5.2.2, 5.2.9, 5.2.21
  8. HMC Section 5.4 p. 260: 5.4.6, 5.4.15
  9. HMC Section 5.5 p. 269: 5.5.9, As in class, compare the power functions of the sign test for the median and the mean test for the mean, if the distribuion is the Laplace.
  10. HMC Section 5.8 p. 294: 5.8.1, 5.8.2, 5.8.4, 5.8.6, 5.8.7, 5.8.11, 5.8.20
  11. HMC Section 5.9 p. 307: Fix the code for the two sample Wilcoxon bootstrap procedures and run it for data on page 302 with 5000 bootstraps. The code is in click , Write similar code for the procedure based on the difference in medians, and run it for data on page 302 with 5000 bootstraps
  12. HMC Section 5.9 p. 308: 5.9.13.
  13. Click for problem .
  14. HMC Section 6.3: 6.3.15 .
  15. HMC Section 6.3: 6.3.16 .
  16. LC Page 67: 5.12, 5.13 .
  17. LC Page 73: 7.5 (assume 2nd derivs), 7.9 .
  18. LC Page 131: 1.17, 1.21 .
  19. LC Page 137: 4.6, 4.8 .
  20. HMC Page 599: 11.3.6, 11.3.7
  21. HMC Page 604: 11.4.1
  22. HMC Page 612: 11.5.2 and 11.5.3
  23. Binomial test: Let X_1, .... , X_n be a random sample from bin(n,p). Show that the likelihood has monotone likelihood ratio in Sum(X_i). Determine, then, the UMP test for p <= p_0 versus p > p_0. For n = 30 what is the randomized 0.05 test.