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Unformatted text preview: ex ) = 1F X ( ex ) . Taking the derivative, f Y ( x ) = d dx F Y ( x ) =f X ( ex )(ex ) , using the chain rule. Since f X = 1, this gives f Y ( x ) = ex , or Y is exponential with parameter 1. For another example, suppose X is N (0 , 1) and Y = X 2 . Then F Y ( x ) = P ( Y x ) = P ( X 2 x ) = P ( x X x ) = P ( X x )P ( X  x ) = F X ( x )F X ( x ) . Taking the derivative and using the chain rule, f Y ( x ) = d dx F Y ( x ) = f X ( x ) 1 2 x f X ( x ) 1 2 x . 32...
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 Spring '10
 ansan
 Degrees Of Freedom

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