e-Statistics > 4480-5480 Probability and Statistics II

## Textbook exercises

Robert V. Hogg, Joseph W. McKean, and Allen T. Craig, Introduction to Mathematical Statistics, 7th ed. [6th ed.] Prentice Hall, NJ.

is an integrated part of your assignment, and supplementary to our course materials covered in class. It is also important for you to complete homework together before quiz. Your work on homework assignment will be considered substantially in grading your quiz when it is submitted before the specified due date. The numbers in [] indicate differently numbered problems in 6th edition.

 Section Reading Assignment Homework 3.1-3.3 Applications of MGF 3.1.25 (MGF of binomial), and 3.3.24 (MGF of gamma; note that ). 3.6 t and F-Distributions 3.6.1-3.6.2, 3.6.8-3.6.10, and 3.6.13 4.4 [5.2 in 6th] "Order Statistics" up to Example 4.4.3 [or 5.2.3 in 6th] (right before the subsection) 4.4.5 and 4.4.9 [5.2.5 and 5.2.9 in 6th] 3.3 -Distributions 3.3.18, 3.3. 19 and 3.3.20 5.1 [4.2 in 6th] Convergence in Probability 5.1.3 and 5.1.5 [4.2.3 and 4.2.4 in 6th] 5.2 [4.3 in 6th] Convergence in Distribution 5.2.2, 5.2.9*, 5.2.10(a)*, 5.3.11* and 5.2.14 [4.3.2, 4.3.9*, 4.3.10(a)*, 4.3.11* and 4.3.14 in 6th] 5.3 [4.4 in 6th] Central limit theorem 5.3.4 and 5.3.5 [4.4.4 and 4.4.5 in 6th] 4.1 [5.1 in 6th] Sampling and statistics Let be independent Bernoulli trials with success probability , and let . (a) Show that is an unbiased estimator of . (b) Find the variance of . 4.2 [5.4 in 6th] Confidence intervals 4.2.7, 4.2.8, 4.2.9, 4.2.11 and 4.2.12 [5.4.2, 5.4.3, 5.4.4, 5.4.6 and 5.4.7 in 6th] 4.6 [5.6 in 6th] Statistical tests 4.6.5, 4.6.6, 4.6.7 and 4.6.8 [5.6.5, 5.6.6, 5.6.7 and 5.6.8 in 6th] 4.7 [5.7 in 6th] Chi-square tests 4.7.4, 4.7.5 and 4.7.9 [5.7.4, 5.7.5 and 5.7.9 in 6th] 6.1 Maximum Likelihood Estimation 6.1.2, 6.1.5 and 6.1.6 [6.1.3(b),(d), 6.1.6 and 6.1.7 in 6th]

(*) Use the result of Central Limit Theorem in Section 5.3.