Just take the derivative and get , valid on [0, 1].
X and Y are both continuous random variables, so for all z. It would be more meaningful to ask for the distribution of , which involves a little bit of work.
how would i find the density function which generates the cdf F(x) = x^(N):
Suppose that x and y are two independent random variables, each of which is uni-
formly distributed on the unit interval [0; 1]. Find the probability that x + y =z for
any z between 0 and 2?
Please I'm kind of desperate I've tried to do the calculations, but can't find where my mistake is !
And , if , that is ; 0 otherwise.
- if z<1, there's no problem, I find zē/2 as the cdf
- if z>1,
by differentiating, it gives the pdf on this part : 1-z, which is negative...
So what's wrong ?