Let T be a full binary tree with 8 leaves. (A full binary tree has every level full). Suppose that two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e number of edges in the unique path between a and b) is ?
My analysis:- The answer should be 4.86 assuming that I do not consider a case wherein two leaf nodes chosen is actually the same leaf node because I assumed that any two nodes are selected together and not in order that is one after other. I do not understand the point of linking independence with choosing the same node twice. I do understand that if we assume two nodes are chosen in order then for independence we do need to necessarily consider the paths of the length 0 but the question mentions nothing about the order and choosing two leaf nodes.
Note that this question has already been answered in a previous post Link of the Post but all the answers mentioned assume that for independence it is necessary to involve a condition wherein two leaf nodes can infact be the same node ie distance 0 node. My point is if we do not choose two leaf nodes in order ie. One after another and rather think of it as two leaf nodes are chosen together then why do we need to include the condition wherein two nodes can be same.