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If the number of arrival in a queue follows the poisson distribution, then the inter-arrival time obeys which one of the following distribution?
- a)Poisson
- b)Negative exponential
- c)Normal
- d)Binomial
Correct answer is option 'B'. Can you explain this answer?
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If the number of arrival in a queue follows the poisson distribution, ...
Explanation:
Poisson Distribution: Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate λ and are independent of the time since the last event.
Inter-arrival Time: The time interval between two consecutive arrivals in a queue is called inter-arrival time.
Negative Exponential Distribution: The negative exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, i.e., a process in which events occur continuously and independently at a constant average rate.
Relation between Poisson Distribution and Negative Exponential Distribution: The inter-arrival time between two consecutive arrivals in a queue is distributed according to the negative exponential distribution if the number of arrivals in the queue follows the Poisson distribution.
Reason: The Poisson process assumes that events occur independently from each other and at a constant average rate. Therefore, the probability of an event occurring in a small time interval is proportional to the length of the time interval. The negative exponential distribution describes the time between events in a Poisson process, where the probability of an event occurring in a small time interval is proportional to the length of the time interval. Hence, the inter-arrival time between two consecutive arrivals in a queue is distributed according to the negative exponential distribution.
Poisson Distribution: Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate λ and are independent of the time since the last event.
Inter-arrival Time: The time interval between two consecutive arrivals in a queue is called inter-arrival time.
Negative Exponential Distribution: The negative exponential distribution is a continuous probability distribution that describes the time between events in a Poisson process, i.e., a process in which events occur continuously and independently at a constant average rate.
Relation between Poisson Distribution and Negative Exponential Distribution: The inter-arrival time between two consecutive arrivals in a queue is distributed according to the negative exponential distribution if the number of arrivals in the queue follows the Poisson distribution.
Reason: The Poisson process assumes that events occur independently from each other and at a constant average rate. Therefore, the probability of an event occurring in a small time interval is proportional to the length of the time interval. The negative exponential distribution describes the time between events in a Poisson process, where the probability of an event occurring in a small time interval is proportional to the length of the time interval. Hence, the inter-arrival time between two consecutive arrivals in a queue is distributed according to the negative exponential distribution.
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If the number of arrival in a queue follows the poisson distribution, then the inter-arrival time obeys which one of the following distribution?a)Poissonb)Negative exponentialc)Normald)BinomialCorrect answer is option 'B'. Can you explain this answer?
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