Abstract: Simple random sampling, both with and without replacement, are fundamental in traditional survey sampling. Based on an idea of ``imaginary census'', we provide in this note a new way for calculating the sample variance of simple sample average, as well as understanding the intrinsic relationship between simple random sampling with and without replacement. The key concept is an ``imaginary census'' matrix, which records the exact sampling trajectory of each draw without replacement, until all population units were sampled out. The random matrix possesses a nice probabilistic symmetry, and each of its column summed to be a fixed number. The new framework, in a sense, is a fusion of two existing classic techniques in traditional survey sampling. One depends on the random vector of 0\,--\,1 valued random variables indicating which population units were sampled, and the other is the symmetrization technique. Our method appears valuable for understanding several important sampling strategies, even to the branch of survey sampling itself. For illustration, we present two examples pertain to unequal probability sampling with replacement and adaptive cluster sampling, with a focus on understanding these sampling strategies from the perspective of simple random sampling.