Cdf of continous RV transformation

  • #1

Homework Statement



Let f(x)= 2x , 0<x<1 , zero elsewhere, be the pdf of X.
Compute the cdf of Y=1/X

Homework Equations



cdf of X = p(X< x)




The Attempt at a Solution



P(1/X <= y)
= P(X <= 1/y)
int 2x from 0 to 1/y
= x^2 eval from 0 to 1/y
= 1/y^2

so the cdf is 1/y^2 for 1<y<infinty

however i don't think this is right.... the text book answers state the cdf as 1-1/y^2


so im confused. thanks for any help!
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
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Since 2 < 4, does this imply that 1/2 < 1/4?

RGV
 

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