Assigned Thursday 1/25 | Read for Tuesday 1/30 Should have read 8.1-8.4 |
#1 - Due for Thursday 2/1 703h1S07.pdf |
Assigned Thursday 2/1 | Read for Tuesday 2/6 Should have read through 8.5.1 |
#2 - Due for Thursday 2/8 1) Find the MLE for the geometric distribution parameter p.
2) This problem uses the logistic regression code on the R-templates
page. |
Assigned Thursday 2/8 | Read for Tuesday 2/13 Should have read all of 8.5 |
#3- Due for Thursday 2/15 This assignment deals with using the geometric distribution to examine the data in problem 8 on page 315. a) Find the formula for the asymptotic variance of the mle for p. b) Estimate p-hat_{mle} for this data. c) Use the asymptotic distribution of the mle to construct an approximate 95-percent confidence interval for p from this data. d) Use the parametric bootstrap with the mle to construct an approximate 95-percent confidence interval for p from this data. (Hint: sort(lhat.dist)[50] andsort(lhat.dist)[950]) |
Assigned Tuesday 2/27 | Read for Thursday 3/1 Should have read 9.1-9.2 |
#4- Due for Tuesday 3/6 Chapter 9: #7 and 8. Also, consider a sample of size 20 and the null hypothesis lambda=1. Find the possible alpha level closest to 0.05 without going exceeding it, and the corresponding rejection region.
Note: You can use R to make a table of Poisson values for a given parameter
with code similar to: |
Assigned Thursday 3/9 | Read for Tuesday 3/20 Should have read 9.3-9.4 |
#5 - Due for Thursday 3/22 A new type of product is supposed to have a mean time until failure of at least 5 hours. A sample of size 8 produced first failure times of 1.6, 4.3, 4.7, 5.8, 6.3, 2.1, 8.5, and 3.2. a) Assuming the failure times follow an exponential distribution, find the UMP test for H0:mean failure time=5 hours versus HA: mean failure time < 5 hours. (Remember that the expected value is 1/lambda). b) Find the p-value for testing these hypotheses with the given data set. (Hint: pgamma) c) Find the power for testing these hypotheses when the true mean failure time is 4 hours. |
Assigned Thursday 4/19 | Read for Tuesday 4/24 Should have read 9.5, 8.7-8.8, 10.1-10.2, 10.4.6 |
#6 - Due for Thursday 4/26 Find the minimum variance that any unbiased estimator of lambda for an exponential distribution can have. Chapter 8: #75 (Identify the natural parameters and sufficient statistic) Chapter 9: #36 |