Advanced Statistical Inference I
Homework 3: Common Families of Distributions Due Date: November 2nd
1. (Engineering Applications) (a) Exercise 3.2(c).
(b) Exercise 3.3.
2. (Business and Law Applications) (a) Exercise 3.8.
(b) Exercise 3.10.
3. (Probability of rare event and statistical reasoning) (a) Exercise 3.5.
(b) Exercise 3.9.
4. (Approximation of probability distribution) (a) Exercise 3.11.
(b) Exercise 3.18.
5. (Hazard rate and modeling) (a) Exercise 3.25.
(b) Exercise 3.26. Also classify those hazard functions in terms of a constant function, an increasing function, or a decreasing function.
6. (Exponential family) Exercise 3.31.
7. (Likelihood ratio and testing) Exercise 3.43.
8. (Useful probability inequalities) (a) Exercise 3.45.
(b) Use (a) to derive a bound on P (X < cnp) where X ∼ binomial(n, p) and 0 < c <
1, a fixed constant.
9. (Stein’s Lemma) Exercise 3.49.
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