A datagram network allows routers to drop packets whenever they need to$.$ The

probability of a router discarding a packet is $p.$ Consider the case of a source host con$-$

nected to the source router, which is connected to the destination router, and then to the

destination host. If either of the routers discards a packet, the source host eventually

times out and tries again. If both host$-$router and router$-$router lines are counted as

hops, what is the mean number of

$($a$)$ hops a packet makes per transmission?

$($b$)$ transmissions a packet makes?

$($c$)$ hops required per received packet?