Q3 (2 marks) The number of telephone calls that arrive at a phone exchange is often modelled as a Poisson random variabl

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Q3 2 Marks The Number Of Telephone Calls That Arrive At A Phone Exchange Is Often Modelled As A Poisson Random Variabl 1 (209.67 KiB) Viewed 127 times

Q3 (2 marks) The number of telephone calls that arrive at a phone exchange is often modelled as a Poisson random variable. Assume that on the average there are 20 calls per hour. X has a Poisson distribution with = 20. The cumulative Poisson distribution probabilities, i.e., P(X sx) are provided below: Cumulative Poisson probabilities (= 20) х P(X <=x) X P(X <= x) 0 0 10 0.0108 1 0 11 0.0214 2 0 12 0.039 3 0 13 0.0661 4 0 14 0.1049 5 0.0001 15 0.1565 6 0.0003 16 0.2211 7 0.0008 17 0.297 8 0.0021 18 0.3814 9 0.005 19 0.4703 a. What is the probability that there are exactly 12 calls in 1 hours? b. What is the average number of calls in 30 minutes?