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week7 - Functions of Random variables In some case we would...

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week 7 1 Functions of Random variables In some case we would like to find the distribution of Y = h ( X ) when the distribution of X is known. Discrete case Examples 1. Let Y = aX + b , a 0 2. Let ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = = = = = = y h x Y x X P y h X P y X h P y Y P y p 1 1 ( ) ( ) ( ) = = = + = = b y a X P y b aX P y Y P 1 2 X Y = ( ) ( ) ( ) ( ) ( ) < = = > = + = = = = = 0 0 0 0 0 2 y if y if X P y if y X P y X P y X P y Y P
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