Re: Discussion Problem_(21)

Posted by Sinistral on May 29, 2013; 6:33am
URL: http://discussion-forum.276.s1.nabble.com/Discussion-Problem-21-tp7581423p7581433.html

let u=x+y; w=y
==> x=u-w & y=w
|J|=1

f(u,w)=2|J|=2 , 0<w<u<2w<2
        =  0 , e.w.

f_u(u)= integral (from u/2 to u) f(u,w) dw     (as w lies between u/2 and u)  where f_u(u) is the marginal pdf of u
        =2u/2 =u          0<u<2

P(X+Y≤1)= P(U<=1)= integral (from 0 to 1) f_u(u) du
                           =  integral (from 0 to 1)   u    du
                           = 1/2