Question) A computer network works by sending a stream of packets from a server to a client computer. Suppose the size of the stream has a Poisson distribution with mean λ = 1000 packets. Sometimes packets are lost in transition. Assume each packet may be independently dropped with probability p = 10-3. (This question is slightly different from the version on the practice exam, please read carefully).
a) What is the probability the client receives an entire stream without any dropped packets on the first pass?
b) The client is able to tell whether an incoming stream is incomplete, and if so, it asks the
server to resend the missing packets. When a packet is resent it is called a retransmission and a missing packet is repeatedly retransmitted until it is received at the client (this is a networking protocol called TCP). For a stream with a fixed length of n packets, what is the expected value and variance of the number of packet retransmissions that will occur before the fill] stream is received at the client? (If the full stream arrives in the first pass, number of retransmissions = 0).
c) For a randomly selected stream, what is the expected value and variance of the number of packet retransmissions that will occur before the full stream is received at the client?