Degree distribution

$2$ points possible $($graded$)$

Consider node j in an Erdos$-$Renyi model $.$ Potentially, it could be connected through edges to up to other nodes, where the presence of each edge is distributed according to Binomial$(,).$ Thus, the degree, $,$ of node is the sum of random variables distributed according to Binomial$(,).$ Therefore, Binomial$(,).$

It follows that the expected value of the degree is

Let be the sum of all node degrees. What is the MLE of in terms of and $?$

unanswered

Do the node degrees follow a power$-$law distribution?