is a standard normal random variable,
and 
is a Chi-Squared random variable with
degrees of freedom, and both of these
random variables are independent, then the distribution of the random
variable 
such that:
(7)If is a standard normal random variable,
and is a Chi-Squared random variable with
degrees of freedom, and both of these
random variables are independent, then the distribution of the random
variable such that:(7)
is said to follow the 
distribution with 
degrees of freedom.
|
Figure 3.7: |
The 
distribution is similar in appearance
to the standard normal distribution (see Figure 3.7). Both of these distributions
are symmetric, reaching a maximum at the mean value of zero. However,
the 
distribution has heavier tails than
the standard normal distribution implying that it has more probability
in the tails. As the degrees of freedom, 
, of the 
distribution approach infinity, the
distribution approaches the standard normal distribution.
See Also:
distribution.