Consider a graph having n = 8 vertices labeled 1,2,..., 8 (see Additional Details at the end of the exam if you are unfamiliar with graphs). Suppose that each edge is independently present with probability p. The degree of vertex i, designated as Di, is the number of edges that have vertex i as one of its vertices. Find Corr(D;, D;), the correlation between D; and Dj. Hint: Decompose D; using r.v. Ij with lij = 1 if edge {i, j} is present.Additional details A graph G is defined as a set of vertices defined as V = {1, ..., n} and a set of edges & C {{i, j } : i, j e {1, ...n}, i # j} that connect vertices. For example, a graph with vertices ) = {1, 2,3, 4} and edges E = {{1, 2}, {2, 3}, {3, 4}, {1,3} } is represented in the figure below. 2 3 For a graph with n vertices, the set of edges is a subset of {{i, j}, i, je {1,...,n}, i * j}. Any set of edges is possible. In Exercise 1 question 3, the set of edges is chosen at random