the statement of the problem: \"Buses arrive at a bus station at a rate 2 buses...

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Statistics

the statement of the problem:
\"Buses arrive at a bus station at a rate 2 buses per minute. thearrival of buses occurs at random times according to a Poissonscatter on (0, infinity). Show all your work for each part.\"
a. what is the probability that no bus arrives between t = 0 andt = 30 seconds?
b. what is the probability that the third bus arrives after t =3 minutes?
c. what is the probability that the 5-th bus arrives within 1minute of the 4-th bus?
d. what is the probability that the 1-st bus arrives in lessthan 1 minute and fewer than 2 buses arrive between t = 3 and t = 5minutes.

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a The average number of bus arrivals is 2 per minute Thereforeper 30 seconds average rate of arrival would be given as 22 1bus per 30sec The probability that no bus arrives between t 0and t 30 sec is computed here as e1 See Answer

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