# PGF of a conditional random variable

#### hemanth

##### New member
I have a queueing system.
The probability Generating Function of the number of packets in the queue (queue length) is given by
$$\displaystyle Q_G(z)=\frac{e^{\lambda T(z-1)}(1-z^{-1})(1-\lambda T)}{1-z^{-1}e^{\lambda T(z-1)}}$$.

I need to find the PGF of a conditional quantity.
$$\displaystyle X=(Q_G|Q_G>0)$$
i.e. to say in words "what is the PGF of queue length given that the queue length is greater than zero".

For a normal random variable X whose Distribution is known this can be defined as
$$\displaystyle F(x|M)=\frac{{P\{X\leq x,M}\}}{P(M)}$$

I am not sure how to proceed whem pmf is not known.