On some discrete random variables arising from recent study on statistical analysis of compressive sensing
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The recent paper [27] provides a statistical analysis for efficient detection of signal components when missing data samples are present. Here we focus our attention to some complex-valued discrete random variables X_l(m,N) (0< l< N-1, 1< M< N), which are closely related to the random variables investigated by LJ. Stanković, S. Stanković and M. Amin in ssa. In particular, by using a combinatorial approach, we prove that for l=0 the expected value of X_l(m,N) is equal to zero, and we deduce the expression for the variance of the random variables X_l(m,N). The same results are also deduced 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 kth moments of U_l(m,N) and V_l(m,N) are equal to zero for every positive integer k which is not divisible by N/(N,l). Moreover, some additional assertions and examples concerning the random variables X_l(m,N), U_l(m,N) and V_l(m,N) are also presented.
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