Stat 452 Fall 2011
Assignment #2
This assignment is due at the beginning of class on Wednesday, October 5, 2011.
1.
Let X be an observation from a N (0, 2 ) population, 2 > 0. Is |X | sucient for 2 ? Justify
your answer.
2.
Exercise 6.2 page 300
3.
Exerci
Stat 452 Fall 2011
Assignment #4
This assignment is due at the beginning of class on Monday, November 21, 2011.
1.
Exercise 7.41 page 363
2.
Exercise 7.44 page 363
3.
Let X1 , . . . , Xn be iid random variables with density
f (x|) =
,
(1 + x)1+
x > 0, > 0
Stat 452 Fall 2011
Assignment #3
This assignment is due at the beginning of class on Wednesday, November 2, 2011.
1.
Recall question 6 on Assignment #2. Let X1 , X2 , . . . , Xn be iid with the geometric
distribution
P (X = x) = (1 )x1 , x = 1, 2, . . . ,
Stat 452 Fall 2011
Assignment #1
This assignment is due at the beginning of class on Monday, September 26, 2011.
1.
Exercise 2.3 page 76
2.
Exericse 2.30 (a), (b), (c) page 80
3.
Exercise 2.35 (a) page 81
4.
Exercise 2.36 page 81
5.
Exercise 4.4 page 192
Stat 452 Fall 2011
Assignment #5
This assignment is due at the beginning of class on Monday, December 5, 2011.
1.
Let X1 , . . . , Xn be iid random variables with probability mass function
P (X1 = x) =
e x
,
x!
x cfw_0, 1, . . ., > 0.
Consider the followi
Statistics 452 Final Exam December 9, 2011
This exam has 110 possible points but will be scored out of 100 points.
This exam has 6 problems and 3 numbered page.
You have 3 hours to complete this exam. Please read all instructions carefully, and check
your
Statistics 452 Fall 2011 Midterm Exam Solutions
1. Since MX (t) = E(etX ) exists for t (h, h) for some h > 0 we know that
MX (0) = E(X ) and MX (0) = E(X 2 ).
Moreover, it is always the case that MX (0) = 1. From the chain rule, it follows that
M (t)
d
lo
Statistics 452 Midterm Exam October 12, 2011
This exam is worth 50 points.
This exam has 3 problems and 1 numbered page.
You have 50 minutes to complete this exam. Please read all instructions carefully, and check
your answers. Show all work neatly and in
Statistics 452 Fall 2011 Final Exam Solutions
1. We will begin by showing that W (X1 , . . . , Xn ) is an unbiased estimator of 2 . This follows
since
E (W (X1 , . . . , Xn ) =
1
1
E (T (T 1) =
E (T 2 ) E (T )
n(n 1)
n(n 1)
1
=
Var (T ) + [E (T )]2 E (T )