2) Supplemental problem. Consider the Wright-Fisher model, in which each generation has N nodes. We consider the time until the lineages of k individuals merge into a common ancestor. Let Xk be the number of generations back until coalescence. In this problem, assume that N is a moderate number. In other words, do not assume that all collisions are two-way collisions. Instead, complicated collisions involving with more than two nodes can occur. a) Assume that k=2. Find the expected coalescence time E(X2) and the probability P(X2=j). b) Assume that k=3. In this problem, assume that N is a moderate number. Find E(X3). Hint: Consider events Ei,i=0,2,3, where there are exactly i lineages collide in the previous generation. Note that E0,E2 and E3 are disjoint and their union is the sample space. Thus, they form a partition of the sample space. Now E(X3)=E(X3E0)P(E0)+E(X3E2)P(E2)+E(X3E3)P(E3) gives us an equality, from which E(X3) can be solved