ISyE 2028A, Summer 2010
Friday June 4
Midterm 1 (Sample) Solutions
1.
Let
1
,,
n
XX
be a random sample from a probability mass function or probability density
function
f
(
x
).
For
k
= 1,2,3,……, the
k
th population moment is denoted by __________,
while the
k
th sample moment is __________.
ANSWER:
1
(
), (1/ )
n
kk
i
i
EX
n
X
=
∑
2.
If
Z
is a standard normal random variable, then
(
2.0)
PZ
≤−
=
__________.
ANSWER:
.0228
3.
Which of the following statements are correct if
2
1,2,.
......
,?
ii
y xi
n
=
∀=
A.
2
yx
=
B.
4
=
C.
22
2
ss
=
D.
4
=
+
ANSWER:
A
4.
If the population distribution of a variable is approximately normal, then according to the
empirical rule, which of the following statement is the most appropriate?
A.
Roughly 68% of the values are within one standard deviation of the mean.
B.
Roughly 95% of the values are within two standard deviations of the mean.
C.
Roughly 99.7% of the values are within three standard deviations of the mean.
D.
All of the above statements are correct.
ANSWER:
D
5.
Answer the following two questions:
a.
If a constant
c
is added to each
i
x
in a sample, yielding
i
y
=
i
x
+
c
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 Summer '07
 SHIM
 Normal Distribution, θ, ISyE 2028A

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