Quiz 4, STAT 5685 Mathematical Statistics II, Spring 2013
Name:
Points:
1. (10 points) Suppose that X1 , . . . , Xn form a random sample from (a, ) distribution with mean a,
and a is known.
(a) (5 points) Does this distribution has MLR in some sucient sta
Quiz 1, STAT 5685 Mathematical Statistics II, Spring 2012
Name:
Points:
1. (10 points) Suppose that X1 , . . . , Xn are iid (, ) variables with unknown > 0 and unknown
> 0.
(a) (5 points) Find a minimal sucient statistic and justify.
(b) (5 points) Show
Quiz 1, STAT 5685 Mathematical Statistics II, Spring 2012
Name:
Points:
1. (10 points) Suppose that X1 , . . . , Xn are iid (, ) variables with unknown > 0 and unknown
> 0.
(a) (5 points) Find a minimal sucient statistic and justify.
(b) (5 points) Show
Quiz 3, STAT 5685 Mathematical Statistics II, Spring 2013
Name:
Points:
1. (10 points) Suppose that X1 , . . . , Xn form a random sample from U (0, ). Let Xn:n be the largest
order statistic.
(a) (5 points) Find the UMVUE of 2 .
2
(b) (5 points) Find E [X
Quiz 2, STAT 5685 Mathematical Statistics II, Spring 2013
Name:
Points:
1. (10 points) Let X be an exponential variable with mean > 0.
(a) (5 points) Find IX (), the Fisher information about in X .
(b) (5 points) Let = 1/ be the rate parameter of the expo
Quiz 1, STAT 5685 Mathematical Statistics II, Spring 2013
Name:
Points:
1. (10 points) Let X1 , . . . , Xn be an iid sample from N (, ), where > 0 is unknown.
(a) (5 points) Does N (, ) belong to the exponential family? Justify.
(b) (5 points) Derive a mi
Solution to Midterm 2, STAT 5685 Mathematical Statistics II, Spring
2013
1. (10 points)
(a) (2 points) It follows from two facts: 1) E () = and 2) Y is complete and sucient statistic.
(b) (3 points) Note that the conditional distribution of X1 given Y = y
Solution to Midterm 1, STAT 5685 Mathematical Statistics II, Spring
2013
1. (10 points)
(a) (2 points) Use Lehmann-Schee Theorem.
(b) (3 points) If Xn is sucient, then there is a function from T to Xn . This is impossible because,
for instance, consider t
STAT 5685
Spring 2013
STAT 5685: Mathematical Statistics II, Spring, 2013
January 22, 2013
Instructor: Jun Yan
Department of Statistics
CLAS 328
860/486-3416
[email protected]
Late homework will not be accepted for any reason.
You are encouraged to discus
Quiz 5, STAT 5685 Mathematical Statistics II, Spring 2013
Name:
Points:
1. (10 points) Suppose that X1 , . . . , Xn form a random sample from N (0, ).
(a) (5 points) Find a variance stabilizing transformation for
n
i=1
n
2
Xi
4
. Note that E (X1 ) = 32 .