Each packet in a congested computer network is lost with probability 1%, independent of other packets. An email message requires 100 packets. If a certain packet is lost, it is retransmitted until it is received.
1. What is the distribution of the number of original data packets that are lost? Give the probability mass function with parameter(s) specified.
2. What is the probability that at least one packet must be retransmitted?
3. What is the probability that two or more original packets must be retransmitted?
4. If there are 10 messages and each contain 100 packets, what is the probability that at least one message requires two or more original packets be retransmitted.