Statistics 24400  Autumn 2016
Final Examination Solution
December 2 and 5, 2016
Name (print):
On my honor, I will not discuss this exam with
ANY PERSON
before 15:30 December
5, 2016.
Signature
1.
Please
print
your name in the space provided. If you are taking this exam on the 2nd or
the morning of the 5th, you must sign the “temporary nondisclosure” line and conduct
yourself accordingly in order to get credit for this final exam.
2.
Do not sit directly next to another student.
3.
Do not turn the page until told to do so.
4.
This is a closed book examination. You are allowed a single page of notes, written on
both sides. Please write your name on your notes and turn it in with the exam. You
are permitted to have a calculator. Devices capable of communication (laptops, tablets,
phones) must be powered down. Tables of the cumulative Normal and
χ
2
distributions
are at the end of the exam.
5.
Please provide the answers in the space and blank pages provided. If you do not have
enough space, please use the back of a nearby page, clearly indicating the identity of
the continued problem.
6.
Be sure to show your calculations.
In order to receive full credit for a problem, you
must show your work and explain your reasoning. Good work can receive substantial
partial credit even if the final answer is incorrect.
7.
Read through the exam before answering any questions. Our scale of credit for questions
may not correlate with the level of di
ffi
culty you experience—use your time wisely!
Question
Points
Score
Question 1
20
Question 2
30
Question 3
30
Question 4
20
TOTAL
100
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
1.
True or False?
(20 pts) There is a “guessing penalty” penalty of four questions (8
pts). You’ll begin to accrue points with your
fifth
correct answer.
(a)
(2 pts)
T
F
If random variables
X
and
Y
are uncorrelated (i.e. Cor(
X, Y
) = 0), then
X
and
Y
must be independent.
F
(b)
(2 pts)
T
F
If
P
(
A
)
< P
(
B
) and
P
(
C
)
>
0, then
P
(
A

C
)
P
(
B

C
).
F
(c)
(2 pts)
T
F
The calculation of
p
value does not depend on the alternative hypothesis once we
know the null hypothesis.
T
(d)
(2 pts)
T
F
The maximum likelihood estimator (MLE) is always unbiased.
F
(e)
(2 pts)
T
F
For any hypothesis testing procedure, it is always possible to increase the power
⇡
= 1

β
while keeping the type 1 error
↵
the same.
F
(f)
(2 pts)
T
F
If
X
is a continuous random variable with cdf
F
(
X
), and
Y
is a random variable
such that
Y
=
F
(
X
), then
Y
is distributed uniformly on [0
,
1].
T
(g)
(2 pts)
T
F
Γ
(
3
2
)
<
Γ
(
1
2
)
T
(h)
(2 pts)
T
F
Fisher’s method of combination on a set of tests of the same hypothesis with
p
values
p
1
, p
2
, . . . p
k
means that the
p
value of the combined tests is given by
P
=
p
1
p
2
. . . p
k
.
F
(i)
(2 pts)
T
F
P
defined as above. Then

2 log
P
⇠
χ
2
2
k
.
T
(j)
(2 pts)
T
F
Suppose that
X
i
⇠
N
(
μ,
σ
2
), with
μ
and
σ
unknown.
Then the distribution of
X
1

μ
does not depend on any unknown parameter.
F
(k)
(2 pts)
T
F
As above, suppose that
X
i
⇠
N
(
μ,
σ
2
) with
μ
and
σ
unknown, Then the distribution
of
X
1

X
2
X
3

X
4
does not depend on any unknown parameter.
T
(l)
(2 pts)
T
F
For a Poisson process, conditional on the number of events
N
(0
,
1] =
n
, the number
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 DRTON
 Statistics

Click to edit the document details