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Apr14-11, 01:05 AM
P: 36
OK, let's see if we can find where my rusty calculus skills betrayed me.

(going to avoid using latex to put in the integral since it seems to come out weird when I preview it)

joint density = e-x1e-x2

we want: integral(0<=X2<=y) of e-x2 times ( integral(0<=X1<=y-x2) of e-x1dx1 ) times dx2

that resolves to: integral(0<=X2<=y) of e-x2 times ( -e-t )t=y-x2t=0 times dx2

which resolves to: integral(0<=X2<=y) of e-x2(1-eye-x2)dx2

we can distribute that out to: ( integral(0<=X2<=y) of e-x2dx2 ) - ( ey * integral(0<=X2<=y) of e-x2e-x2dx2 )

after we integrate we get: ( -e-t )t=yt=0 - ey( (-1/2)e-2t )t=yt=0

which gives: 1-e-y + (1/2)ey(1-e-2y)

a little quick distribution turns that into: 1 - e-y + (1/2)(ey-e-y)

which finally gives us: 1 + (1/2)ey - (3/2)e-y

...not what we're supposed to get.