$4.$ Consider the Stop and Wait protocol, where transmissions occur on an unreliable channel with bit error probability $\backslash ($ p$\_\{$b$\}\backslash )$ that is independent from bit to bit. All packets are of a fixed size $\backslash ($ N $\backslash ),$ and all acks are of a fixed size $\backslash ($ L $\backslash ).$

$($a$)$ Find probability $\backslash (\backslash$alpha $\backslash )$ of a packet being in error, and probability $\backslash (\backslash$beta $\backslash )$ of an ack being in error. $(5$pt$)$

$($b$)$ What is the probability $\backslash ($ x $\backslash )$ that a packet or an ack is in error? $(5$pt$)$

$($c$)$ Using the above two results, find the maximum achievable throughput of Stop and Wait. Carefully state all your assumptions. $(10$pt$)$