Cars arrive at a vehicle equipment inspection station according to a Poisson Process with rate a = 8 per hourSuppose that the probability is p 0.3 that an arriving car will have no equipment violations(a) What is the probability that exactly 8 cars arrive during the hour and all 8 have no violations?(b) For any fixed number x > 8, what is the probability that x arrive during the hour of which 8 have noviolation?(c) What is the probability that 8 "no-violation" cars arrive during the next hour?

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Asked Nov 6, 2019
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Cars arrive at a vehicle equipment inspection station according to a Poisson Process with rate a = 8 per hour
Suppose that the probability is p 0.3 that an arriving car will have no equipment violations
(a) What is the probability that exactly 8 cars arrive during the hour and all 8 have no violations?
(b) For any fixed number x > 8, what is the probability that x arrive during the hour of which 8 have no
violation?
(c) What is the probability that 8 "no-violation" cars arrive during the next hour?
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Cars arrive at a vehicle equipment inspection station according to a Poisson Process with rate a = 8 per hour Suppose that the probability is p 0.3 that an arriving car will have no equipment violations (a) What is the probability that exactly 8 cars arrive during the hour and all 8 have no violations? (b) For any fixed number x > 8, what is the probability that x arrive during the hour of which 8 have no violation? (c) What is the probability that 8 "no-violation" cars arrive during the next hour?

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Expert Answer

Step 1

Poisson Arrival process:

The probability Px of x packet arrivals in a time interval α is given by:

 

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P(Xx)aeia x! where 2=mean number of occurences in the interval e Euler's constant 2.71828 a time interval

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Step 2

(a)Computing the probability that exactly 8 cars arrive during the hour and all 8 have no violations.

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P(X 0(No violation P(No violation X 8)P(X = 8) (8x1)6 (0.3) 8! -S (8 e 8 (0.3) 8! =0.000009

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Step 3

b) Computing the probability that x arrive during the hou...

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P((X (8 No violati on))= P(8 No violation X = x) P(X =x) x) (8) e (0.3) (1-0.3) x! 8 -8 (8) e x! (0.3) (x-8)8! x! e$2.4 8(x-8)

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