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IEOR 4404
Assignment #4
Simulation
October 1, 2008
Prof. Mariana OlveraCravioto
Page 1 of 2
Assignment #4
– due October 7th, 2008
1. Give inversetransform, acceptancerejection, and composition algorithms for generating from
each of the following densities. Discuss which algorithm is preferable for each density. (First
plot the densities).
(a)
f
(
x
) =
(
3
x
2
2
,
if

1
≤
x
≤
1
,
0
,
otherwise.
(b) For 0
< a <
1
/
2,
f
(
x
) =
x
a
(1

a
)
,
if 0
≤
x
≤
a,
1
1

a
,
if
a
≤
x
≤
(1

a
)
,
1

x
a
(1

a
)
,
if 1

a
≤
x
≤
1
,
0
,
otherwise.
2. Using the composition method, give algorithms for generating random variables from the
following distributions.
(a)
F
(
x
) = (
x
+
x
3
+
x
5
)
/
3, for 0
≤
x
≤
1
(b)
F
(
x
) =
(
1

e

2
x
+2
x
3
,
if 0
< x <
1
3

e

2
x
3
,
if 1
< x <
∞
(c)
F
(
x
) =
∑
n
i
=1
α
i
x
i
, for 0
≤
x
≤
1, where
α
i
≥
0,
∑
n
i
=1
α
i
= 1.
3. A pair of fair dice are to be continually rolled until all the possible outcomes 2
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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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