7FunctionsofaRV

# 7FunctionsofaRV - Functions of a RV Jeffrey B Burl Click to...

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Click to edit Master subtitle style  EE 3180 Probability and  Functions of a RV Jeffrey B. Burl 11

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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)  and g(x). 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 33 -5 -4 -3 -2 -1 0 1 2 3 4 5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x g(x)

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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  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 - - = = -
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