Having a little trouble with functions of random variables

[bennyska]

Homework Statement

Let X ~UNIF(0,1), and Y=1-e^-x. Find the PDF of Y

Homework Equations

The Attempt at a Solution

So i have Fy=Pr(Y<y)
=Pr(1-e^-x<y)
=Pr(-e^-x<y-1)
=Pr(e^-x>1-y)
=Pr(-x>ln(1-y)
=pr(x<-ln(1-y)
=Fx(-ln(1-y))
(here is where I'm having a breakdown)
=x|0 to -ln(1-y) which doesn't really make sense... (that's my notation for evaluate from 0 to...)
i'm having a similar problem, and i think if i can get this figured out, i'll be able to do that one as well.

 

[vela]

OK, so you got

$$F(y) = \int_0^{-\log (1-y)} dx = -\log (1-y)$$

Why do you think it doesn't make sense?

 

[bennyska]

i was making a few dumb mistakes. got it taken care of. thanks.