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Packets arrive at a certain node on the university’s intranet at 10 packets per minute, on...

Packets arrive at a certain node on the university’s intranet at 10 packets per minute, on average. Assume packet arrivals meet the assumptions of a Poisson process.

  1. Calculate the probability that exactly 15 packets arrive in the next 2 minutes.
  2. Calculate the probability that more than 60 packets arrive in the next 5 minutes.
  3. Calculate the probability that the next packet will arrive in within 15 seconds. (all answers 3 decimal places)
Math   Statistics-And-Probability   
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Answer #1

Let X be the random variable denoting Packets arrive at a certain node on the university’s intranet.

So X ~ Poisson (10) per minute

1) the probability that exactly 15 packets arrive in the next 2 minutes

X ~ Poisson (20) per 2 minute

= 0.052

2) the probability that more than 60 packets arrive in the next 5 minutes

X ~ Poisson (50) per 5 minute

3)the probability that the next packet will arrive in within 15 seconds.

X ~ Poisson (2.5) per 15 seconds

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