The random variables $X$ and $Y$ have the following density function:
$f(x,y) = C.{e^{-x/2y}e^{-3y}\over y}$ if $0<x<\infty, 0<y< \infty$ and $0$ otherwise.
Find $E(X|Y=2017)$.
I did $\int_o^\infty xC.{e^{-x/2y}e^{-3y}\over y}dx= e^{-6051}C\int_0^\infty {e^{-x\over4034}\over2017} = 2Ce^{-6051}$
If I did the integration correct, I need to find C but I couldn't figure out how to find it. Any help is appreciated.
I have given the solution in handwritten image and I hope it is clear and legible