  In this paper we give a generalization of the discrete complex-valued random
variable defined and investigated in \cite{ssa} and \cite{m8}. We prove the
statements concerning the expressions for the excepted value and the variance
of this random variable.
  In partucular, such a random variable here is defined for each of $m$ rows of
any $m\times N$ complex or real matrix ${\rm{\bf A}}$ with $1\le m\le N$. We
consider the arithmetic mean $\bar{X}(m)$ of these $m$ random variables and we
deduce the expressions for the expected value $\Bbb E[\bar{X}(m)]$ and the
variance ${\rm{ Var}}[\bar{X}(m)]$ of $\bar{X}(m)$. Using the expression for
${\rm{ Var}}[\bar{X}(m)]$, we establish some equalities and inequalities
involving ${\rm{Var}}[\bar{X}(m)]$, the Frobenius norm, the largest eigenvalue,
the largest singular value and the coherence of a matrix ${\rm{\bf A}}$. It is
showed that some of these estimates are closely related to the Welch bound of
the coherence of a $m\times N$ complex or real matrix ${\rm{\bf A}}$ with $1\le
m\le N$. Taking into account that the value of coherence of the measurement
matrix in the theory of compressive sensing has a significant role, we believe
that our results should be useful for some topics of this theory.
