Y=sin(x)
let X~uniform[0,pi/2]
compute density of fy(y) for Y.
my attempt
------------
arcsin(Y) = X
fx(arcsinY)
-------------- = sqrt(1-y^2) * fx(arcsinY)
(1/sqrt(1-y^2))
then
/\ arcsin(pi/2) sqrt(1-y^2) * fx(arcsinY) dy
\
.\
\/ arcsin(0)
/\ infinity sqrt(1-y^2) * fx(arcsinY) dy
\
.\
\/ 0
and i am stuck here as i cannot evaluate this, i probably did something wrong earlier...
Have you understood any of my posts on this topic?
My expression for G(y) in this thread comes from using exactly the same approach that I explained in more detail here: http://www.mathhelpforum.com/math-he...ge-159842.html. Have you read it? What don't you understand?
As for where the 2/pi comes from, you said that X~uniform[0,pi/2]. Are you familiar with the pdf of a continuous uniform distribution? (I assumed that you were).
Simply differentiate the cdf I gave in my previous reply.
I intended the answer I gave here:
http://www.mathhelpforum.com/math-he...ge-159842.html
to be an example you could follow when trying to answer other similar questions. Please try to apply each step of that answer to the current problem. Show all your work, say where you get stuck.
You do exactly the same as if you were finding .