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### Normal Random Variable

If we take a an affine transformation of a standard Normal random variable: Y=aZ+b the new density of Y is

This is called the Normal variable with parameters, b and a2, denoted by .

For any such transformation we have: if , then the density of Y is

The two parameters that are needed to define a normal are: , , this explanation will be developed in chapter 6.

In general if you have a Normal random variable with parameters and , we need to standardize it, because the probabilities cannot be computed from a closed form formula, this is done by standardizing, say

Now is a standard variable so we can use the distribution function

A web site that allows you to look up some probabilities for Normal distributions:

Susan Holmes
1998-12-07