Please show me specific process of the answer. I really have no idea how to do t

Question

Please show me specific process of the answer.

I really have no idea how to do this question

it is very helpful for me to prepare for my final.

Thank u so much !

Question 4: Suppose that a Poisson process provides a good model for telephone calls arriving at a help line at the rate of two per minute. (a) (2 marks). What is the probability that five calls arrive in the next two minutes? (b) (1 mark). What is the probability that five calls arrive in the next two minutes and then five more calls arrive in the following two minutes? (c) (1 mark). What is the probability that no calls will arrive during a ten-minute period?

Explanation / Answer

Solution:

Solution of part (a)

Let X denote call that arrive in two minutes. Here X is poisson with = 4

P(X) = (e-4 × 45)/5! = 0.156

Solution of part (b)

Since all call arrive independently, most probably five call arrives in two minutes and then five more call arrives in following two minutes, which means

0.156 × 0.156 = 0.0244

Solution of part (c)

LetY denote number of call that arrive in 10 minutes. Here Y is poisson with = 20

P(Y = 0) = (e-20 × 200)/0! = 2.06 × 10-9

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