- #1
Dwolfson
- 9
- 0
I am stumped.
I have that W=X+Y+Z and that S=X+Y
These are all X, Y, & Z and Independent and Uniformly Distributed on (0,1)
I found the pdf of S to be (Assume all these < rep. less than or equal to):
S when 0<S<1
2-S when 0<S<1
So I continued:
To do pdf of S+Z=W
I figured there will be 3 intervals:
when 0<W<1, 1<W<2, and 2<W<3:
I Have figured out the one from 0<W<1
to be integral from 0 to W pdf(w)=S(pdf(W-S))ds
= W^2/2
For the other two intervals I am struggling on which pdf of S to use and what is the interval of integration..
Thank you in advance for your help,
--Derek
I have that W=X+Y+Z and that S=X+Y
These are all X, Y, & Z and Independent and Uniformly Distributed on (0,1)
I found the pdf of S to be (Assume all these < rep. less than or equal to):
S when 0<S<1
2-S when 0<S<1
So I continued:
To do pdf of S+Z=W
I figured there will be 3 intervals:
when 0<W<1, 1<W<2, and 2<W<3:
I Have figured out the one from 0<W<1
to be integral from 0 to W pdf(w)=S(pdf(W-S))ds
= W^2/2
For the other two intervals I am struggling on which pdf of S to use and what is the interval of integration..
Thank you in advance for your help,
--Derek