[glossary Contents] [Previous File] [Next File]

- Normal:
A random variable X is normally distributed if its density
function is
*exactly*of the form: - Standard normal random variable (usually called Z) is the special case Z ~ N(0,1)
- Chi-square distribution or
Let Z1, Z2, ... , Zk be k
*independent*standard normal random variables. Then the function - t-distribution or
Let Z ~ N(0,1) and C ~
where Z and C
are
*indendent*. Then the function -
follows the
distribution.
- F distribution or : Let and be indpendently distributed. Then the function

follows the follows the distribution. - F distribution or : Let and be indpendently distributed. Then the function

where is the mean of X and is the variance of X.

We indicate that X is a normal random variable by writing: X ~ N( , )

follows the chi-squared distribution with

- A linear combination of normal random variables is also
normally distributed. Let
be m
normally distributed random variables, and let
be
m constants. Then the random variable

is also normally distributed. - If X and Y are both normal then Cov[X,Y] = 0 X and Y independent.

Document Last revised: 1997/1/5