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Midterm 2 Exam STAT 211-505 (Type A)
March 25, 2008
Name :
UIN:
Important: read the following instructions carefully.
•
Do not sit directly next to another student.
•
Do not turn the page until told to do so.
•
This is a closed book examination. You may use your calculator, and one double-sided sheet of formulas that
you have brought with you. You should have no other printed or written material with you on the exam.
•
Fill out all the information on both the scantron and your exam papers.
•
Mark the correct choice using a soft (No. 2) pencil. Sheets completed with pens or hard pencils can not be
read by scanning machines.
•
Do not fold, bend or make stray marks on your scantron form.
•
If you are unsure of what a question is asking for,
do not hesitate to ask the instructor for clariFcation
.
•
Your scantron won’t be returned to you, so it is a good idea that you mark your choices on your exam papers
as well to have a copy of your answers.
•
Turn in your answer sheet along with the exam when you are done.
•
This exam has 5 pages (17 questions total). It is your responsibility to make sure you have all 5 pages.
•
Each question is worth 6 points. If you get all of the correct, you will receive 102 points.
1

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1. A clinic needs 3 nurses and 3 doctors to handle incoming patients properly. The joint probability model for
the number of nurses (
X
) and doctors (
Y
) that show up on any given day is given below.
Y
0
1
2
3
0
0.3
0.15
0.02
0.01
1
0.2
0.05
0.01
0.01
X
2
0.1
0.05
0.02
0.01
3
0.01
0.02
0.03
0.01
What is the probability that more than three total staF (nurses and doctors) will show up on any given day?
A. 0.01
B. 0.18
C. 0.10
D. 0.08
E. 0.90
2. In the previous problem, are
X
and
Y
independent?
A. Yes because
P
(
X
= 3
,Y
= 3)
n
=
P
(
X
= 3)
P
(
Y
= 3)
B. Yes because
P
(
X
= 3
,Y
= 1) =
P
(
X
= 2
,Y
= 0)
P
(
X
= 1
,Y
= 0)
C. No because
P
(
X
= 0
,Y
= 0)
n
=
P
(
X
= 0)
P
(
Y
= 0)
D. No because
P
(
X
= 0
,Y
= 0)
n
=
P
(
X
= 1)
P
(
Y
= 1)
E. Yes because
P
(
X
= 1) =
P
(
Y
= 1)
3. In the previous problem, what is the expected number of nurses that show up on a given day?
A. 0.403
B. 0.84
C. 0.5
D. 1.5
E. 2
4. In the previous problem, suppose we record the number of nurses and doctors that show up every day for
64 days. What is the expected diFerence between the average number of nurses and the average number of
doctors that show up for 64 days?

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