Problem $2[15$ points$]$: Consider sending a large amount of data over a lossy link. Each

bit can be independently in error with a probability of $p.$ Each packet consists of two parts:

data and header parts. Packets with any bit $($data or header$)$ in error are dropped by

the receiver. Each packet contains $h$ bit headers and $d$ bits data. The raw capacity of the

link is $C$ bits per second.

$($a$)$ What is the probability that a packet gets dropped at the receiver?

$($b$)$ Compute the throughput over the link. Throughput is defined as the maximum num$-$

ber of data bits received per second by the application. Assume that the sender is

sending packets back$-$to$-$back.

$($c$)$ Assume $h=100$ and $p={10}^{-5}.$ What is the value of $d$ that maximizes the throughput

over the link? You can use calculator or other online tools.