M4L1
Functions of Single Random Variables
1. Introduction
This is the first lecture on functions of Random Variables
.
Different functions of Random
Variable along with their properties are discussed. Determination of pdf and CDF of those
functions are also discussed.
2. Functions of Random Variable
As discussed in Module 3, Random Variable (RV) is a function that maps the outcomes of an
experiment over a sample space to a numerical value on the real line. Any function of
, say
, is also a Random Variable, denoted as
.
Formally this function is defined as, a function of single random variable,
, which is a
composite function of
with domain set
of experimental outcomes
(Papoulis and Pillai, 2002).
For an outcome
is a number and
as another number specified in terms of
and
X
g
. Now the function of a random variable
at
can be represented as
and
value of this number can be taken as:
as assigned to Random Variable, Y.
Thus a function of random variable is a composite function
with
domain set, S of experimental outcomes. The CDF of
,
for the Random Variable
(function of
), defines the probability of the event
consists of all outcomes,
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 Spring '13
 Dr.RajibMaity
 Civil Engineering, Probability distribution, Probability theory, probability density function, Cumulative distribution function

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