ISyE 2027 Probability with Applications
Polly B. He
Fall10, Week 9
Reading: Section 8.18.4
Transforming Discrete Random Variables
Given a function of a random variable, we want to obtain the new distribution function and
the probability mass function (or density function for the continuous case).
Example 8.1.1 Consider an airplane with 150 seats. The number of customers has a discrete
uniform distribution, say
P
(
X
=
j
) = 1
/
200
, j
= 1
,
2
, . . . ,
200.
Let
Y
be the number of
customers being turned away. Calculate the distribution function and the probability mass
function for
Y
.
Transforming Continuous Random Variables
A simple example: Let
X
be the temperature expressed in degrees Celsius, then
Y
=
9
5
X
+32
is the temperature in degrees Fahrenheit. If we know the distribution function of
X
(call
it
F
X
) and the corresponding density function
f
X
, what are the distribution and density
functions of
Y
?
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Rules for changeofunits transformation.
Let
X
be a continuous random variable with
distribution function
F
X
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Zahrn
 Probability theory, Distribution function, probability density function, Polly B. He Fall10

Click to edit the document details