$1$ Consider a Go$-$Back$-$N protocol over a two$-$state Markov channel, where the average number of consecutive

good slots is $100$ and the average number of consecutive bad slots is $100/9.$ The packet error probability is

$1$ for a bad slot and $0$ for a good slot, respectively. The round$-$trip time is m $=2$ slots, i$.$e$.,$ a packet that is

erroneous in slot t will be retransmitted in slot t $+2.$

$($a$)$ Compute the throughput that could be obtained if packets were directly transmitted over the channel

without using any protocol

$($b$)$ Compute the throughput of the Go$-$Back$-$N protocol for an error$-$free feedback channel

$($c$)$ Compute the throughput of the Go$-$Back$-$N protocol for a feedback channel subject to iid errors with

probability $0\mathrm{.}1.$