|Assigned Thursday 1/25||Read for Tuesday 1/30
Should have read 8.1-8.4
|#1 - Due for Thursday 2/1|
|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
|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-hatmle 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) andsort(lhat.dist))
|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