The random variable X has density given with
(x+1)/2 , -1<x<1
0, in other cases
find the density of the random variable Y=1-X^2
I'm stuck with this problem
any help would be appreciated
yes, I'm aware of that. I used it, and don't know how to solve it completely.
After I integrate it, I have: (1/4)x^2 + x/2 + C, -1<x<1,
and because in the main formula : y=1-x^2, i have x squared, when I calculate the root, I'll have both signs, plus and minus, in front of the square root.
I don't know how to handle these two cases in one.
So I'm given the density (x+1)/2
To find out the function of distribution, I integrate it
integrate (x+1)/2 dx - Wolfram|Alpha
what do I do next?
I dont know what exactly is your answer you are showing me.
I need hint on what to do next after this step.
I know that eventually I'll use Py(x)=|Px(f[-1](x))*|f[-1](x)|
but I'm having problems with the domain, because I have a square in the equation, and the domain of x can be negative.
Thanx for the help so far
why is g^-1(x) = SQRT(1 - x)
but not = + - SQRT(1-x)
after i substitute the values in the formula for the PDF of Y, do I get:
g(y) =[(sqrt(1-x)+1)/2 ]*[1/2*sqrt(1-x)]