
69Random Variables, Distributions, Moments, and Statistics
A normally distributed sample is symmetric. That is to say, the mean is equal to the median.
Very commonly, the data are not symmetrical; that is, there is higher frequency left or right of the
mean. Two important cases: positive (mean < median) or values biased toward the right and negative
(median < mean) or biased toward the left.
Standard Normal
The standard normal RV, denoted by Z, has zero mean, that is to say μ
z
= E(Z) = 0, and standard
deviation and variance equal to unity, that is to say σ
Z
= 1. We write the pdf as p(Z) = N
0,1
(Z) and
simplify the normal or Gaussian to be
Nz
z
01 ...