Then the data matrix is
with three rows and two columns.
We now present some descriptive statistics. We will begin with the mean vectors.
3.3 Mean Vectors
Let be
random variables, where
denotes the transpose of a matrix. The expected value of the random
vector is defined as the vector of expectations i.e.
More generally, if is a matrix of random variables, then the
is the matrix of expectations with elements
, i.e.:
For a random vector , the mean vector consists of the means of each variable:
where . For example let
be
measurements on the first variable. Then the sample mean for the first variable
is defined as follows:
The sample mean can be computed from the measurements on each of the
variables. Therefore, in general for
sample means, we have: