# Probability and conditional expectation

• March 14th 2011, 03:57 AM
ulysses123
Probability and conditional expectation
Y and V are independant, $E[V]=0$, $E[Y^2]<\infty$

$X$ $=c+$ $aY^2$ $+bV$
a,b,c are constant.

Find $E[X/Y]$

I get $E[X/Y]$ $=c$ $+$ $aE[Y^2 /Y]$

Not sure if this is right
• March 14th 2011, 07:48 AM
Moo
Hello,

If Y and V are independent, then E[V|Y]=E[V] and for a suitable function f, E[f(Y)|Y]=f(Y).

So there's just 1 simplification left.
• March 14th 2011, 02:46 PM
ulysses123
why does E[f(y)/y]=f(y)?

in this case i would have thought that since f(y) depends explicitly on the values of y, this cannot be the case
• March 15th 2011, 02:19 AM
Moo
It IS the case... f(Y) is Y-measurable.