GATE ME 2018 Set 2 — Question 34
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Engineering Mathematics → Statistics & Distributions → Poisson Distribution
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Question
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of 30 customers/hour. The probability that the time between successive customer arrival is between 1 and 3 minutes is _______ (correct to two decimal places).
Correct answer
0.36 to 0.4
Solution
If the arrival of customers follows a Poisson distribution with rate , then the time between successive arrivals follows an exponential distribution with the same rate .
Given .
The probability density function (PDF) for the time between arrivals is:We need to find the probability :Using and :
Given .
The probability density function (PDF) for the time between arrivals is:We need to find the probability :Using and :
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