It is intended to participate in the substantive biological and medical research requiring nontrivial novel developments in probability and/or statistics. A special effort will be made to obtain solutions of the mathematical problems generated by such substantive studies. The substantive problems considered for the immediate future can be exemplified by the following: (1) Study of evolution conducted on the level of macromolecules; (2) Optimal statistical tests for the effects of treatments taking into account specifically that the possible variable response of the experimental animals (this is a modification of "Model II analysis of variance" problems, especially concerned with non-normal distribution); (3) Mechanism of differences in virulence of bacteria that form chains; (4) Mechanism of carcinogenesis; (5) A variety of problems of health/statistics that concern cause-specific death rates in the presence of competing risks.