10NOV05
M566
DUE THURSDAY 17NOV05
When YOU want to establish that a statistics t : E F is minimal sucient for
a dominated statistical model (P P(E)| ) do the following:
Since the model is dominated we can choose the -nite measure upon which all
the probab
09NOV05
M566
HOMEWORK 10
DUE THURSDAY 01DEC05
Problem 1. Let N be a nite non-empty set. Consider the statistical model
(GN P(RN )| R+ ), where G, denotes the Gamma distribution with shape
+
,
parameter > 0 and scale > 0.
It is well-known (earlier homework
03NOV05
M566
HOMEWORK 8
DUE THURSDAY 10NOV05
In all the dominated statistical models below the Likelihood function is assumed
to be selected in a way that makes most sense when construction the ML estimator(s) in a dominated model (P P(E)| ). When you ans
27OCT05
M566
HOMEWORK 7
DUE THURSDAY 03NOV05
Problem 1. Let x (x | N ) be a nite family of independent and identical
distributed observables each following a distribution P on R or on a subset of R.
In each subproblem below state the statistical model and
28SEP05
M566
HOMEWORK 5
DUE THURSDAY 06OCT05
Last Homework in pure probability
Problem 1. Let the observable x R+ follow the Gamma distribution P with
shape parameter > 0, i.e., consider this Gamma distribution on R+ . The dis1
tribution of the observable
05OCT05
M566
HOMEWORK 6
DUE TUESDAY 18OCT05
Problem 1. Let x (x | N ) be independent identical distributed observables,
each following the Bernoulli distribution Bp on cfw_0, 1 with the probability of getting
outcome 1 being p, where p ]0, 1[ is unknown.
21SEP05
M566
HOMEWORK 4
DUE THURSDAY 29SEP05
Problem 1. Let (E, A) be a measurable space, P a probability measure on (E, A),
D A a measurable subset with P (D) > 0 and P (Dc ) > 0. Let t 1D : E cfw_0, 1
be the indicator function corresponding to D, i.e.,
09NOV05
M566
FINAL TAKE HOME EXAM
DUE MONDAY 12DEC05 before 10:00AM
Several daughters (cows) from two top rated bulls, Ferdinand and Hugo, from the
Danish Bull station The Happy Half Cow were observed wrt. the amount of
their daily milk production. The sp
08SEP05
M566
HOMEWORK 2
DUE THURSDAY 15SEP05, BUT POSTPONED UNTIL TUESDAY
20SEP05
Problem 1. Let Pi Pi , be the gamma distributions with shape parameter
i > 0 and scale > 0, i = 1, 2, and let t : R R R R be the mapping dened
by
t(x1 , x2 ) :=
(x1 + x2 , x
15SEP05
M566
HOMEWORK 3
DUE THURSDAY 22SEP05
Problem 1. Let (E, A) and (F, B) be measurable spaces and let Py be a probability
measure on the measurable space (E, A), y F . Suppose that Py has density fy
wrt a nite measure on (E, A), y F , i.e., Py (A) =
01SEP05
M566
HOMEWORK 1
DUE THURSDAY 08SEP05
Terminology: Let E be a set. If there exists a one to one correspondence between
E and the positive natural numbers N := cfw_1, 2, 3, the set is is called a countable
set. The number of elements in a set E is
10OCT05
M566
EXAM 1
TAKE HOME
DUE FRIDAY 27OCT05
This is the take home Exam 1. It OK to work together if you want and to ask me
any questions you like (concerning this Exam and M566 in general). The important
thing is that you work on these problems. Alth