7FunctionsofaRV - Click to edit Master subtitle style EE...

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Unformatted text preview: Click to edit Master subtitle style EE 3180 Probability and Functions of a RV Jeffrey B. Burl EE 3180 Probability and 11 EE 3180 Probability and Function of a RV n Y=g(X) is a random variable. n We are interested in computing probabilities, distribution functions, and density functions for this new variable. n Consider the distribution function: n Write the distribution function of Y in terms of Fx(x) EE 3180 Probability and 22 ( ) Pr( ) Pr( ( ) ) y F y Y y g X y = = ( ) g X y F Pr( ) y X R F EE 3180 Probability and Example EE 3180 Probability and 33-5-4-3-2-1 1 2 3 4 5-2-1.5-1-0.5 0.5 1 1.5 2 x g(x) EE 3180 Probability and Example 1: Y = ax + b n To find Fy(y), first need to find the values of x s. t. n If a > 0, then for n If a < 0, then for EE 3180 Probability and 44 ax b y + ( ) Pr y x y b y b F y X F a a-- = = ax b y + y b x a- ax b y + y b x a- ( ) Pr 1 y x y b y b F y X F a a-- = = - EE 3180 Probability and...
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This note was uploaded on 06/16/2010 for the course EE ee3180 taught by Professor Burl during the Spring '10 term at Michigan Technological University.

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7FunctionsofaRV - Click to edit Master subtitle style EE...

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