q1 Consider one - persistent CSMA. There are two contending stations having a packet ready, and both listen on the channel for an ongoing transmission of a third station to finish. What is the probability that the two contenders will collide? Give it as a number between 0 and 1. q2 Consider the same setting as in the previous question, but now with p - persistent CSMA for some probability value 0 < p < 1. Please find an expression for the probability that both contenders collide. Assume that they are statistically independent. You will need to: work out the probability that they collide in the first time slot, the probability that they collide in the second time slot, the probability that they collide in the k-th time slot etc., combine these probabilities using the law of total probability, and when calculating the end result you will need the sum formula for the (infinite) geometric series.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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q1 Consider one - persistent CSMA. There are two contending stations having a packet ready, and both listen on the
channel for an ongoing transmission of a third station to finish. What is the probability that the two contenders will
collide? Give it as a number between 0 and 1. q2 Consider the same setting as in the previous question, but now with p
- persistent CSMA for some probability value 0 < p < 1. Please find an expression for the probability that both
contenders collide. Assume that they are statistically independent. You will need to: work out the probability that they
collide in the first time slot, the probability that they collide in the second time slot, the probability that they collide in the
k-th time slot etc., combine these probabilities using the law of total probability, and when calculating the end result you
will need the sum formula for the (infinite) geometric series.
Transcribed Image Text:q1 Consider one - persistent CSMA. There are two contending stations having a packet ready, and both listen on the channel for an ongoing transmission of a third station to finish. What is the probability that the two contenders will collide? Give it as a number between 0 and 1. q2 Consider the same setting as in the previous question, but now with p - persistent CSMA for some probability value 0 < p < 1. Please find an expression for the probability that both contenders collide. Assume that they are statistically independent. You will need to: work out the probability that they collide in the first time slot, the probability that they collide in the second time slot, the probability that they collide in the k-th time slot etc., combine these probabilities using the law of total probability, and when calculating the end result you will need the sum formula for the (infinite) geometric series.
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