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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?
Just take the derivative and get, valid on [0, 1].
X and Y are both continuous random variables, sofor all z. It would be more meaningful to ask for the distribution of
, which involves a little bit of work.
If I recall correctly f(z)=z on (0,1) and 2-z on (1,2)
Please I'm kind of desperate :D 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 ? :(
You forgot to deal with the case whereI think.
Well the probability would be 0, wouldn't it ?
More like 1 minus that :)Quote:
Originally Posted by Moo
Oh yeah right, now I can see through it ! Thanks !Quote:
Originally Posted by theodds
It's easier to use geometry and see the triangles,
including the ones for the complement when 1<z<2
This is a uniform distribution on the unit square.
I like conditional stuff and dislike graphic stuff, hence the tortuous method (Giggle)Quote:
Originally Posted by matheagle
so its 0 or 1?