Discussion Problem_(29)

[duck]

Suppose the joint pdf of X and Y is given by:
f(x,y) = e^(-x-y) for 0<x<∞ , 0<y<∞
         = 0 elsewhere.
Find P(X+Y≤0)

[rohan]

zero

[laracroft]

Hey Duck

Please explain this one to me... I always get stuck on PDF amd PMFs...

Plz HELP !!

[Sumit]

zero..

[Kuldeep]

zero

[Devika]

Hey! Someone please explain! I think i've taken the wrong integral limits :s

[Sinistral]

Devika wrote

Hey! Someone please explain! I think i've taken the wrong integral limits :s

we need to integrate f(x,y) over the region which is bounded by the limits 0<x<∞ , 0<y<∞ AND x+y≤0. It can be clearly seen that the former is the Ist quadrant and the latter will never go in the Ist quadrant. Hence no region to integrate over. therefore 0

[Devika]

And all this while I thought it was X +Y <=1. *slaps forehead*
Thanks :)