Stat 544 Final Exam
May 1, 2007
I have neither given nor received unauthorized assistance on this examination.
signature l. A classic example in the Bates and Watts non-linear regression text concerns the "Rumford cooling
experiment," where after friction
yrs
1. Below are tables giving pmfs f (x I 6) for an observable X , for a parameter 6 with possible
values 1,2, and 3 . Then there is a table giving a pmf g(6) for a simple discrete prior distribution
for the parameter.
ID/é; a) Suppose that a single ob
1. Suppose that a parameter 0 = (61,02) takes one of the values in {(1,0),(2,l],(2,3)}. Then X
4 4
is unifome distributed on {0,1,2} if 61 =1
is Binomial (2,02) if 61 = 2
A Bayesian uses prior probabilities
g<w>=agaza=awgala};
a) In the table below give t
l/véY Qiié' Fina l
1. Below is a directed acyclic graph that represents a joint distribution for the variables
a,pl,p2,p3,Xl,X2, andX3.
(m5)
/l\.
Some information about this joint distribution is that:
a and ,8 are independent, a ~ Exp(l), ~ Exp (1)
condi
All of the Gamma distributions in this homework solution are based on the shape parameter
alpha and inverse scale parameter beta, i.e. X~Gamma(alpha,beta) has pdf
STAT544
Homework 1
2008-02-05
Keys
GCS&R 2.1
Ans:
Suppose that the prior distribution for is
Stat 544 Exam 2
May 5, 2008
I have neither given nor received unauthorized assistance on this examination.
<61
signature
name printed
There are 10parts on this exam. I will score every part out of 10 points. 1. Suppose that Y :(l/H,Y12,Y21,Y22) can be m
Stat 544 Exam 2
April 30, 2012
(corrected version)
I have neither given nor received unauthorized assistance on this examination.
6
Signature
Name Printed
There are 14 parts on this exam. I will score every part out of 10 points and count your
best 10 sco
STAT544
Homework 2
2008-02-17
Keys
1
Ans:
(a) X1 , ., XN Poisson(i ), i = 1, ., N . M Ucfw_1, ., N , 1 Exp(1) and 2 Exp(1). Let
Sm = m Xi , T = SN and X = (X1 , ., XN ). Since,
i=1
(M, 1 , 2 |X) f (X|M, 1 , 2 ) (M )(1 )(2 )
Sm e(m+1)1 T Sm e(N m+1)2 ,
1