UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 1- Solutions
Winter 2015
Issued: Thursday, January 9
Due: Tuesday, January 20
Problem 1.1
h Pn
i
2
i=1 (Xi )
)2 = E
)2 =
(a) We have that E (X
.
Given
independence,
E
(
X
2
n
Pn

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 2 Solutions
Winter 2015
Problem 2.1
By commutativity of the product, we can write
p (x) =
n
Y
p (xi ) =
i=1
n
Y
p (x(i) )
i=1
hence by factorization theorem the order statistics i

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 4
Winter 2015
Issued: Saturday, January 31
Due: Tuesday, February 10
This problem set is worth 75 points.
Recall that a symmetric matrix Rdd is
- positive semidefinite (PSD) if aT

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 8
Winter 2015
Issued: Saturday, February 28
Due: Thursday, March 12
This problem set is worth 90 points.
Problem 8.1 (15 points)
Keener 8.23.
Solution 8.1
iid
The setup: X1 , . .

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 6
Winter 2015
Issued: Saturday, February 14
Due: Thursday, February 26
This problem set is worth 60 points.
Problem 6.1 (20 points)
Find conjugate distributions for the following

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 7
Winter 2015
Issued: Saturday, February 12
Due: Thursday, March 5
This problem set is worth 90 points.
Problem 7.1 (15 points)
iid
Keener 7.11: Consider a Bayesian model where Un

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 3- Solutions
Fall 2015
Problem 3.1
We have
p (x, y) =
Y
p (xi , yi ) =
i
2 n
1cfw_max(xi + yi ) < 1cfw_max xi > 0, max yi > 0
i
i
2
It follows from the factorization theorem tha

UCLA
Department of Statistics
STAT 200B: Theoretical Statistics
Problem Set 5
Winter 2015
Issued: Friday, February 6
Due: Thursday, February 19
This problem set is worth 75 points.
Solution 5.1
Differentiating the CDF gives the PDF of Pareto distribution