I have the following question: Consider a random graph on nvertices, where between any two vertices there is an edge with probability p = c/n, (alternatively, no edge with probability 1-p) all edges are independent. Using the characteristic functions find limit in distribution of the degree of a vertex (i.e., the number of incident edge at this vertex) in the graph.
I think I am on the right track when I am assuming that the random variable X which denotes the degree of a random vertex is distributed according Bin(n, c/n) hence this would mean we can solce this question by utilizing the generating function of the binomial distrubtion.
Are my assumptions correct? And if yes, can you provide a complete solution to the question? I would be very thankful! :)
I am also thinking like this:
Let p(x) denote the number of vertices in the graph which is n. Then there are n-1 edges(2 dots that get connected wich gives 1 edge), hence y is then Bernoulli(c/n) and if you sum (n-1) random variables with this distribution you get Bin(n-1, c/n).
But once again, not sure if this is correct.