Random Variable Definition

# Random Variable - Random Variable X(s = x s REAL LINE x Random Variable X is a mapping that maps each outcome s in the sample space to a unique

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Random Variable Random Variable X is a mapping that maps each outcome s in the sample space to a unique real number x , x −∞ < < ∞ . You must specify how the mapping X operates. ” Let X be the random variable indicating the number of packets waiting ….” X is a binary random variable. X=1 if the outcome satisfies …” Sometimes the outcome itself is a real number. In that case, X simply shows the outcome. REAL LINE s x () Xs x =

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Example- Bernoulli Toss a biased coin which shows head with probability p. Define random variable X as 1 0 if the outcome is a head X otherwise =
Mapping Terminology Range (of the random variable X ) {: () } X S x x X s for some s S = = In general, X is a many-to-one mapping. Inverse Operation 1 Xx : for any X xS , 1 () {: () } X x s Xs x = Inverse Image 1 XJ : for any X JS , 1 ( ) {: () } X J s Xs J = We make use of the fact that 1 [ ] [{ : ( )}] PX J P s s X J ∈= REAL LINE s x

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Example- Bernoulli
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## This note was uploaded on 11/23/2010 for the course EE EE528 taught by Professor Majungsoo during the Spring '10 term at Korea Advanced Institute of Science and Technology.

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Random Variable - Random Variable X(s = x s REAL LINE x Random Variable X is a mapping that maps each outcome s in the sample space to a unique

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