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contribution general expression derived probability density time recent common ancestor tmrca simple birthdeath tree widely used stochastic nullmodel biological speciation extinction conditioned constant birth death rates number extant lineages density contrasted previous result obtained using uniform prior time origin new distribution applied two problems phylogenetic interest first probability number taxa existing time past tree known number extant species given birth death rates second determining tmrca two randomly selected taxa unobserved tree produced simple birthonly yule process latter case assumed rate bifurcation speciation size number tips known shown lead closedform analytical expression probability distribution parameter arrived based known mathematical form age distribution yule trees given size branching rate derived de novo similar distribution additionally conditioned tree age new distribution exact yule prior divergence times pairs taxa stated conditions potentially useful statistical bayesian inference studies phylogenies