Probability And Random Variable Lecture(5)
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1 Random Variable (r.v): A random variable is a function whose domain is the set S of all experimental outcomes. A finite single valued function that maps the set of all experimental outcomes into the set of real numbers R is said to be a r.v, if the set is an event for every x in R. ) ( X S ) ( | x X PILLAI
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Transcript of Probability And Random Variable Lecture(5)
1
Random Variable (r.v): A random variable is a function whose domain is the set S of all experimental outcomes.
A finite single valued function that maps the set of all experimental outcomes into the set of real numbers R is said to be a r.v, if the set is an event for every x in R.
) ( XS
)(| xX
PILLAI
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Conditions for a function to be Random Variable
• Every point in S must correspond to only one value of the random variable.
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Probability Distribution function
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xXPxxF )(
This is known as probability distribution function of a random variable.
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Probability density function
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Derivative of the distribution function is known as probability density function (pdf).
.
)()(
dx
xdFxf X
X
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Additional Properties of a PDF
If for some then
This follows, since implies is the null set, and for any will be a subset of the null set.
We have
0)( 0 xFX ,0x . ,0)( 0xxxFX (3-15)
0)()( 00 xXPxFX 0)( xX
)( ,0 xXxx
).(1 )( xFxXP X (3-16)
, )( )( xXxX
PILLAI
Example
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Solution
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