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The recent paper [27] provides a statistical analysis for efficient detectionof signal components when missing data samples are present. Here we focus ourattention to some complex-valued discrete random variables $X_l(m,N)$ ($0\lel\le N-1$, $1\le M\le N$), which are closely related to the random variablesinvestigated by LJ. Stankovi\'c, S. Stankovi\'c and M. Amin in \cite{ssa}. Inparticular, by using a combinatorial approach, we prove that for $l\not=0$ theexpected value of $X_l(m,N)$ is equal to zero, and we deduce the expression forthe variance of the random variables $X_l(m,N)$. The same results are alsodeduced for the real part $U_l(m,N)$ and the imaginary part $V_l(m,N)$ of$X_l(m,N)$, as well as the facts that the $k$th moments of $U_l(m,N)$ and$V_l(m,N)$ are equal to zero for every positive integer $k$ which is notdivisible by $N/\gcd(N,l)$. Moreover, some additional assertions and examplesconcerning the random variables $X_l(m,N)$, $U_l(m,N)$ and $V_l(m,N)$ are alsopresented.

On some discrete random variables arising from recent study on statistical analysis of compressive sensing