43. Consider a graph having a vertices labeled 1, 2, n, and suppose that between each of the pairs of distinct vertices an edge is, independently, present with probability p. The degree of vertex i, designated as D,, is the number of edges that have vertex i as one of its vertices.

(a) What is the distribution of D₁?

(b) Find p(D,, Dj), the correlation between D; and Dj.