Stochastic properties of previously introduced one parameter discrete model of genetic diversity (M. Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887-894 (1998)) are investigated. Two approaches are compared: (A) when the on-step substitution number and/or the number of substitution steps are random variables; (B) referred parameters are replaced by mathematical expectations of the respective variables. It has been demonstrated, that estimations of sequence measure based on the number of replication steps are more under the assumption of case (A) as compared with (B). Thus, real biological situation relating to the case (A) could additionally promote the increasing of distinctions between different taxons (e.g. HIV, etc.). Peculiarities of one-parameter discrete model of genetic diversity during calculation of the distinctions between symbol (e.g. nucleotide) sequence sets are also discussed.