Conditional variance

Hi,

I am not too good in statistics;
yet I have to evaluate the conditional variance of a random variable with
known mean and variance.
apparently
Var(X |X<q) = E([X - E(X|X<q)]^2 |X<q)
This is a function in q.

My question is:
Can this function be written as:

var(q) = int_{-inf}^q (x- mux(q))^2 f(x) dx

where: f(x) is the pdf of the random variable
and mux(q) is the conditional mean:
mux(q)= int_{-inf}^q x f(x)dx

Along the same line, I also need to evaluate the conditional variance:
var(q) = var((X - q) P | X > q )
where P is a second random variable which is correlated positively to X.
Any help appreciated.

--
Xavier Brusset
PhD
UCL
.