Recall the Medium Access Control $($MAC$)$ Protocol discussed in lecture $($at the end of Sec V$\mathrm{.}6.)$ We saw

that each time slot could be in one of three states: I $($idle$),$ C $($collision$)$ or S $($Success$).$ Consider here that

there are $6$ nodes who want to send packets and that all of the nodes act independently of one another $($the

example in lecture had $5$ nodes$).$ Each node has a probability p $=0\mathrm{.}4$ of being active in a time slot. Let

Y be the random variable that denotes the number of nodes that are active in a time slot. For an idle slot

Y $=0,$ for a successful slot Y $=1,$ and if Y $>=2$ the slot has a collision.