1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability random vector, transformation

  1. Oct 8, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f(x,y) = e^(-x-y), 0<x< infinity, 0<y<infinity, zero elsewhere, be the pdf of X and Y. Then if Z = X + Y, compute P(Z<=0), P(Z,<=6), and, more generally P(Z<=z), for 0<z<infinity. What is the pdf of Z?

    2. Relevant equations

    P(x,y) = ∫∫(f(x,y) dxdy


    3. The attempt at a solution

    so, P(Z<= 0 ) is pretty obviously 0

    P(Z<=6) = P(X+Y <= 6)
    =P(X<=6-Y)

    into equation

    ∫from (0 to infinty) ∫ from (0 to 6-Y ) e^(-x-y) dx dy

    -e^(-x-y) eval from 0 to 6-Y
    = (-e^-6 ) + e^-y

    ∫from (0 to infinity) (-e^-6 ) + e^-y dy
    = -ye^(-6) -e^-y eval from (0 to infinity)
    = -infinity -0 - ( 0 - 1)
    = - infinity

    so, im definitly going wrong somewhere because a probability of negative infinity makes no sense... I know this could be done using a different method of tranformations, but i think im supposed to do something along these lines because thats what is taught in the preceeding chapter.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?