properties of conditional expectations first, everyone, property, something

vagabond

Hi everyone,

I have two independent random variables 'a' and 'b' and when I multiply these two guys I have a new random variable 'x'.

I'm after the conditional expectation of 'x' given that I know one of the variables, let's assume 'b'.

i.e. I'm after,

E(x|b)

My question is am I "allowed" to do something like this:

E(x|b) = E(a*b|b) = E(a|b) * E(b|b)

The reason for the mix-up is that the first property of conditional expectations is that they are linear in 'x' but this is not applicable to me is it?

cheers guys,

Matori

No longer a problem, the above should hold because 'a' and 'b' are independent