Economics 430: Homework 1 Fall 2019, UCLA
Due Date: Oct 9, 2019
All problems require detailed worked out solutions to receive full credit. All problems are worth the same.
1. Evans & Rosenthal: 4.3.13
2. Evans & Rosenthal: 4.4.19
3. Assume that X1,…,X9 are i.i.d. having Bernoulli distribution with parameter p. Suppose that we wish to test the hypotheses
H0 ∶p=0.4 H1 ∶p≠0.4
Let Y = ∑9i=1 Xi.
(a) Find c1 and c2 such that P(Y ≤ c1∣p = 0.4)+P(Y ≥ c2∣p = 0.4) is as close as possible to
0.1 without being larger than 0.1.
(b) Let δ be he test that rejects H0 if either Y ≤c1 or Y ≥c2. What is the size of the test
δc?
(c) Draw a graph of the power function δc.
4. The file ‘Prob4 data.txt’ contains 50 observations from a Gamma distribution with unknown parameters α and β.
(a) Plot a histogram of the data and overlay the respective density curve.
(b) Compute the Method of Moments estimates of the parameters, α̂ and β̂.
(c) Generate 1000 new samples from your data and compute the Bootstrap Mean, standard errors, and 95% confidence intervals of the parameters and compare them against your results from part (b).
5. Evans & Rosenthal: 5.4.12
6. Evans & Rosenthal: 5.5.18
7. Evans & Rosenthal: 6.2.17
8. Evans & Rosenthal: 6.2.25
9. Evans & Rosenthal: 6.3.22
10. Evans & Rosenthal: 6.4.17