MS&E 352
Handout #2
Decision Analysis II
January 6
th
, 2009
Problem Set 0
Due: January 13, 2009
________________________________________________________________________
1 of 6
This problem set is a gentle tutorial to the beta distribution, which we shall use
extensively in this class. You will need Excel to complete the assignments. Please take a
screen capture of your Excel graphs and tables for each assignment, put it in a word
document and submit it on Coursework (Submit Homework).
BETA DISTRIBUTION
A long time ago, a mathematician developed magical powers and put a spell on his
children such that they would have mathematical desires. While other children ask for
gifts, these children ask for distributions. It is New Year’s Eve, and daddy has promised
one gift for all three children.
John:
Daddy, I want a uniform distribution, and I want it right now.
Sally:
I like bell curves, please daddy, give me a bell curve.
Tom:
Daddy, I really want to stretch the bell curve! I love making it wide and then
narrow.
Daddy:
Alright, alright. I will satisfy all of you. You will get the
beta distribution!
John:
Huh? What’s a beta distribution?
Daddy:
It is a magical distribution that can satisfy all three desires. It has the following
probability density function (pdf):
0
0,
,
)
1
(
)
,
(
1
)
,
;
(
1
1

=


β
α
β
α
β
α
β
α
x
x
B
x
f
and B is the beta function.
Sally:
What’s the beta function?
Daddy:
It is the Euler integral of the first kind, defined by:
∫



=
1
0
1
1
)
1
(
)
,
(
dt
t
t
y
x
B
y
x
, for Re(x), Re(y) > 0
Tom:
This looks quite scary Daddy! Why should we care?
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 Winter '09
 RONHOWARD
 Normal Distribution, Probability theory, probability density function, Cumulative distribution function, Daddy, Beta distribution

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