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Integration of random variables

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data

    f(x,y)= (4/5)(x+3y)exp(-x-2y) for x,y, >0

    Find E[Y|X]

    2. Relevant equations

    E[Y|X] =integral y *f_xy (x,y)/ f_x (x) dy

    3. The attempt at a solution

    f_x (x) = integral [o,∞] [4/5](x+3y)exp(-x-2y) dx = (2x+3)/(5exp(x))

    When taking the integral of y[(4/5)(x+3y)exp(-x-2y)] / [(2x+3)/(5exp(x)) ] dy dx for [0,∞] for y (x+3)/(2x+3) is that correct?
    Last edited: Nov 4, 2012
  2. jcsd
  3. Nov 4, 2012 #2
    well, if it's conditional, and it's dependent on x, shouldn't your outcome be a function of x?
  4. Nov 4, 2012 #3
    Oh my bad, I just got mixed up with definitions. Thanks! <3
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