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13. Random Graphs. In this problem we will revisit Random Graphs on n vertiees, which are created as follows: . Create anew graph 62 (RE) with |V| :n. t For each possible pair of vertices i, j on the graph. ip a coin with probability of heads equal to p. If it eomes up heads, create an edge between i and j. 1, For a given vertex 1:, what is its expected degree? 2. What is the probability that the degree of a vertex is at least 1'? ED 3. Let X be a random variable representing the number of edges on the graph. What is ELY]? U 4. Your friend creates a random graph with n = 6 vertices using a coin with bias p (where p is unknown to you). You observe that the resulting graph has 3 edges on it. What is the maximum likelihood estimate (MLE) of p? U 5. A triangle in a graph is a set of three vertices. t'