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Statistics

Figure 4.14 Standard normal pdf.

The normal distribution is best-known through its probability density
function (pdf) which has the well-known bell-form, see Fig. 4.14. Such a
pdf can be considered as a continuous, theoretical form of a histogram.
The mathematical equation of the general normal pdf is:

1 2 ð x2μÞ 2
f ðxÞ 5 p ffiffiffiffiffiffi e 2σ 2 (4.21)
σ 2π
This function has two parameters: μ and σ . 0. For each value of
these parameters, one has another normal pdf. It can be shown that the
mean or average of a normal pdf is μ and its standard deviation is σ.
Moreover, this function is symmetric with respect to its average. The
relation between the general normal pdf, with variable x, and the stan-
dard normal pdf, with variable z is z 5 (x 2 μ)/σ. Clearly the standard
normal distribution has mean 0 and standard deviation equal to 1, see
Fig. 4.14.
The distribution function of a normal distribution is given in
Fig. 4.15. Note that this is not a discrete function and not an observed
function, but a theoretical, continuous function.