# Normal distribution

1. Aug 27, 2008

### Einstein

A normal distribution can be completely defined by two parameters - the mean and the standard deviation. Given a normal distribution however, say X, how can I use just the mean and the standard deviation to give me conditional expected values for X<=0 and for X>0? Im guessing the distribution can be standardised to obtain a z-statistic.

2. Aug 27, 2008

"Given a normal distribution however, say X" - I assume you mean that the variable $$X$$ has a normal distribution. Are both $$\mu$$ and $$\sigma$$ known?

"how can I use just the mean and the standard deviation to give me conditional expected values for $$X \le 0$$ and for $$X>0$$ ?"
This doesn't make sense to me as it stands. In statistics we take expected values of some function of a random variable - can you elaborate on what it is you seek?

3. Aug 27, 2008

### HallsofIvy

If X has normal distribution with mean $\mu$ and standard deviation $\sigma$ then $z= (x- \mu)/\sigma$ has the standard normal distribution. As statdad said, "conditional expected values for X< 0 and X> 0" makes no sense." I might interpret as "suppose X a standard normal distribution, restricted to be larger than 0. What is the the expected value of X?"

That would be
$$\frac{1}{\sqrt{\pi}}\int_0^\infty x e^{-x^2}dx= \frac{1}{2\sqrt{\pi}}$$
The general problem, with non-zero mean or standard deviation not 1 would be a much harder integral.

Last edited by a moderator: Aug 27, 2008