Size bias occurs famously in waiting-time paradoxes, undesirably in sampling schemes, and unexpectedly in connection with Stein’s method, tightness, analysis of the lognormal distribution, Skorohod embedding, infinite divisibility, branching processes, and number theory. In this paper we review the basics and survey some of these unexpected connections.
"Size bias for one and all." Probab. Surveys 16 1 - 61, 2019. https://doi.org/10.1214/13-PS221