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IEOR 4404
Assignment #9
Simulation
November 20, 2006
Prof. Mariana OlveraCravioto
Page 1 of 2
Assignment #9
– due November 17th, 2006
1. (From Ross) Let
X
(
n
) and
S
2
(
n
) be the sample mean and sample variance of a sample of
size
n
of iid random variables
X
1
,. .. ,X
n
.
(a) Verify that the following recursions hold:
X
(
n
+ 1) =
X
(
n
) +
X
n
+1

X
(
n
)
n
+ 1
and
S
2
(
n
+ 1) =
±
1

1
n
²
S
2
(
n
) + (
n
+ 1)(
X
(
n
+ 1)

X
(
n
))
2
(b) Write a program that uses the recursions given above to calculate the sample mean and
sample variance of a data set.
2. (From Ross) Continue to generate standard normal random variables until you have generated
n
of them, where
n
≥
100 is such that
p
S
2
(
n
)
/n <
0
.
1, where
S
2
(
n
) is the sample variance
of the
n
data values.
(a) How many normals do you think will be generated?
(b) How many normals did you generate?
(c) What is the sample mean of all the normals generated?
(d) What is the sample variance?
(e) Comment on the results of (c) and (d). Were they surprising?
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This note was uploaded on 11/17/2010 for the course IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.
 Spring '10
 C

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