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Marginal density, integration problem.

qwertykeyboards · 2009-05-19 09:22:43

if joint probability density function fx,y (x,y) = 4xe^-(x+y) where 0<x<y whats fx of X? i think it should be integral from 0 up to x of 4xe^-(x+y) dy but when i work it out i get a different answer to the one given. i get 4xe^-x (-e^-x + 1) but solution is apparently just 4xe^-2x. any help appreciated.

19-05-2009 9:22am

#1

qwertykeyboards

Closed Accounts Posts: 48 ✭

Join Date: June 2007

Posts: 28

if joint probability density function fx,y (x,y) = 4xe^-(x+y) where 0<x<y

whats fx of X?

i think it should be integral from 0 up to x of 4xe^-(x+y) dy
but when i work it out i get a different answer to the one given. i get 4xe^-x (-e^-x + 1) but solution is apparently just 4xe^-2x.

any help appreciated.

0

Comments

#2 19-05-2009 10:50am

Fremen

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Posts: 2356

If X<Y, shouldn't you be integrating from X to infinity?

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#3 19-05-2009 11:23am

qwertykeyboards

Closed Accounts Posts: 48 ✭

Join Date: June 2007

Posts: 28

yeah your right, figured it out as soon as i posted the question. thanks for your help.

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