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Unformatted text preview: tion of another. Suppose Y = g (X ) for some function g and
a random variable X with a known pdf, and suppose we want to describe the distribution of Y. A
general way to approach this problem is the following three step procedure:
Step 1: Scope the problem. Identify the support of X. Sketch the pdf of X and sketch g.
Identify the support of Y. Determine whether Y is a continuoustype or discretetype random
variable. Then take a breath–you’ve done very important ground work here.
Step 2: Find the CDF of Y. Use the deﬁnition of the CDF: For any constant c,
FY (c) = P {Y ≤ c} = P {g (X ) ≤ c}. In order to ﬁnd the probability of the event {g (X ) ≤ c},
try to describe it in a way that involves X in a simple way. In Step 2 most of the work is
usually in ﬁnding FY (c) for values of c that are in the support of Y.
Step 3: Diﬀerentiate FY to ﬁnd its derivative, which is fY . Typically the pdf gives a more
intuitive idea about the distribution of Y than the CDF. 3.8. FUNCTIONS OF A RAND...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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