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IE 230
Seat # ________
Name ___ < KEY > ___
Please read these directions.
Closed book and notes. 60 minutes.
Covers through the normal distribution, Section 4.7 of Montgomery and Runger, fourth edition.
Cover page and four pages of exam.
Page 8 of the Concise Notes.
No calculator. No need to simplify beyond probability concepts.
For example, unsimplified factorials, integrals, sums, and algebra receive full credit.
Throughout,
f
denotes probability mass function or probability density function
and
F
denotes cumulative distribution function.
A trueorfalse statement is true only if it always true; any counterexample makes it false.
For one point, write your name neatly on this cover page and circle your family name.
Score ___________________________
Exam #2, March 8, 2011
Schmeiser
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Name _______________________
Closed book and notes. 60 minutes.
For statements a—g, choose true or false, or leave blank.
(three points if correct, one point if left blank, zero points if incorrect)
(a) T
F
←
The continuousuniform family of distributions is a special case of
the discreteuniform family.
(b)
T
F
←
Scheduled arrivals, such as to physician’s office, are naturally
modeled with a Poisson process.
(c) T
F
←
Consider a discrete random variable
X
with probability mass function
f
X
. Then
∫
−∞
∞
f
X
(
c
)
dc
=
1.
(d) T
F
←
Consider a random variable
X
with Poisson distribution with mean
μ =
3 arrivals. Because
σ
X
2
= μ
, the units of
σ
X
are arrivals
1
/
2
.
(e) T
←
F
If
Z
is a standardnormal random variable, then P(
Z
=
0)
=
0.
(f) T
F
←
If
Z
is a standardnormal random variable, then
f
Z
(0)
=
0, where
f
Z
is
the probability density function of
Z
.
(g) T
F
←
If
Z
is a standardnormal random variable, then
F
Z
(
−
3.2)
=
F
Z
(3.2),
where
F
Z
is the cdf of
Z
.
2. Suppose that the random variable
X
has the discrete uniform distribution over the set
{1, 2,.
.., 10} and that the random variable
Y
has the continuous uniform distribution over
the set [1,10].
For statements a–e, choose true or false.
(a)
(3 points) T
←
F
E(
X
)
=
E(
Y
).
(b)
(3 points) T
F
←
V(
X
)
=
V(
Y
).
(c)
(3 points) T
F
←
F
X
(5.5)
=
F
Y
(5).
(d)
(3 points) T
F
←
f
X
(5.5)
=
f
Y
(5).
(e)
(3 points) T
←
F
P(
X
=
5)
=
f
X
(5).
Exam #2, March 8, 2011
Page 1 of 4
Schmeiser
Name _______________________
3. (from Montgomery and Runger, 4–50) For a battery in a laptop computer under common
conditions, the time from being fully charged until needing to be recharged is normally
distributed with mean 260 minutes and a standard deviation of 50 minutes.
(a) (8 points) Sketch (well) the corresponding normal pdf. Label and scale both axes.
____________________________________________________________
Sketch the usual bell curve, with center at 260 minutes
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This note was uploaded on 04/25/2011 for the course IE 230 taught by Professor Xangi during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Xangi

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