Consider sending a large amount of data over a lossy link. Each bit can be independently in error with a probability of b. Packets with any bit (data or header) in error are dropped by the receiver. Each packet contains an h bit header and a d-bit data payload. 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 number of data bits received per second by the application. Assume that the sender is sending packets back-to-back.

(c) Assume h = 100 and b = 10^-5 . What is the value of d that maximizes the throughput over the link? Do not use a program to find the answer. Use algebra and calculus; show your work.