A total of $n$ , $n>0$,nodes are placed on a 2D plane.To determine the links be these nodes ,sequential experiments of coin tosses are conducted as follows:
For each pair of nodes , a coin is randomly chosen from a box of a sufficiently large number of coins and then tossed . If the head appears, a link is drawn to connect the two nodes .
After the toss , the coin is returned to the box and the experiment repeats for the next pair.Note that due to production problems at the mint ,all coins in the box are biased. The probability of head is different for different coins ,but it can be assumed to follow a $U[0.4,0.8]$
Question:
The set of nodes and the links thus drawn between them constitute a random graph . Let $X$ be the number of links in the graph.What is $f(x)$,$E[X]$,$V[X]$,$M_X(t)$?
An isolated node is formed if it is not connected to any other nodes in the graph Let $Y$ be the number of isolated nodes in the graph.What is $E[Y]$?
I don't know the question whether can use $Wald's equation$ to solve $E[X],V[X]$ Assume each node be connected success be 0 fail be 1 $Ber(Y)$ and and $E[E[X|Y]]=>(C^n_2*E[X]) $ will get $E[X]$ .Is right or not? I don't know how to derive the pmf.