Integration of random variables

[nikki92]

Homework Statement

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

Find E[Y|X]

Homework Equations

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

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?

 

[phiiota]

well, if it's conditional, and it's dependent on x, shouldn't your outcome be a function of x?

 

[nikki92]

Oh my bad, I just got mixed up with definitions. Thanks! <3