Consider a discrete time branching process {Xn​} with probabili... | Filo

SOLVED:Consider a branching process with generation sizes Zn satisfying Z0=1 and P(Z1=0)=0. Pick two individuals at random (with replacement) from the nth generation and let L be the index of the generation which contains their most recent common ancestor. Show that ℙ(L=r)=𝔼(Zr^-1)- E(Zr+1^-1) for 0 ≤r<n. What can be said if P(Z1=0)>0 ?

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