We do a case study of two different analysis techniques for studying the stochastic behavior of a randomized system/algorithms: (i) The first approach can be broadly termed as a mean value analysis (MVA), where the evolution of the mean state is studied assuming that the system always actually resides in the mean state. (ii) The second approach looks at the probability distribution function of the system states at any time instance, thus studying the evolution of the (probability mass) distribution function (EoDF).