Stat 531, Mathematical Statistics II, HW #8
Spring 2012
Due: Monday, April 16
1. 7.4.1
X ~ Binomial(2, ). Show that for any function g(X), E(g(X) = 0 => g(X)=0.
2. 7.4.2 (a)
3. 7.5.2
4. 7.5.6
5. 7.5.10
6. 7.6.1
7. 7.7.3
To show the other 5 statistics are
Stat 531, Mathematical Statistics II, HW #10
Spring 2012
Due: Monday, April 30
1. 8.1.4
2. 8.1.10
3. 8.2.2
4. 8.2.9
This example illustrates how we determine the sample size to achieve a given
power. The test statistic will be the sample mean, whose sampl
Stat 531, Mathematical Statistics II, HW #9
Spring 2012
Due: Monday, April 23
1. 7.8.1 (c)
Note that by Theorem 7.3.2 (p. 381) and the definition of minimal sufficiency, we
can say that: if a sufficient statistic exists and if MLE also exits uniquely, the
Stat 531, Mathematical Statistics II, HW #6
Spring 2012
Due: Monday, March 19
1. Correction for Midterm 1. (You can skip it if the mistake was minor.)
2. 6.3.3
3. 6.3.15
4. 6.3.18
5. Consider random samples from Cauchy distribution:
(a) Let = 2, use R fun
Stat 531, Mathematical Statistics II, HW #5
Spring 2012
Due: Noon, Friday, March 2
I moved the due date so that you will work on this assignment first, then the take-home Midterm
exam.
1. 6.2.1
2. 6.2.7
3. 6.2.8
The following question will show up in the
Stat 531, Mathematical Statistics II, HW #7
Spring 2012
Due: Monday, April 9
The following questions were assigned by Prof. Jernigan during my two-week long sick leave.
The amount of the questions is equivalent to 2 assignments.
1. 7.1.2
2. 7.1.5
3. 7.1.6
Stat 531, Mathematical Statistics II, HW #4
Spring 2012
Due: Monday, Feb. 27
1. 6.1.1
2. 6.1.5
3. 6.1.9
4. Find the MLE for the regression coefficients a simple linear regression model:
,
where are iid. Normal.
Midterm exam is scheduled on Wednesday, Feb.
Stat 531, Mathematical Statistics II, HW #3
Spring 2012
Due: Monday, Feb. 20
1. 5.5.3
Recall that the power function is a function of the parameter (). In this case,
has 2 values.
2. 5.5.5
Hint: rewrite the rejection rule into a relatively simple inequal
Stat 531, Mathematical Statistics II, HW #2
Spring 2012
Due: Monday, Feb. 13
1. 5.2.3
Extra credit for part (d). Read section 5.2.2 (p. 245) for details.
2. 5.2.6
3. 5.2.8
4. 5.2.11
Use the result from class note.
5. 5.2.17
Clearly write out the support o
Stat 531, Mathematical Statistics II, HW #1
Spring 2012
Due: Wed, Feb. 1
1. 4.3.18
Note that Yn = maxcfw_X1; ; Xn, and find the cdf Yn. Also, recall that .
2. 4.4.9
Hint: Let X be the number of observations (out of 72 samples) that less than 3.
What is th