In a multi-user operating system, 30 requests are made to use a particular…
2018
In a multi-user operating system, 30 requests are made to use a particular resource per hour, on an average. The probability that no requests are made in 40 minutes, when arrival pattern is a poisson distribution, is _________.
- A.
e−15
- B.
1−e−15
- C.
1−e−20
- D.
e−20
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Correct answer: D
Key idea: For a Poisson process with mean λ over an interval, the probability of k events is P(k) = e^{-λ} λ^{k} / k!. For zero events this simplifies to P(0) = e^{-λ}.
Compute the rate: 30 requests per hour = 30/60 = 0.5 requests per minute.
Mean in 40 minutes: λ = 0.5 × 40 = 20.
Probability of zero requests: P(0) = e^{-λ} = e^{-20} ≈ 2.06 × 10^{-9}.
Therefore the required probability is e^{-20}.
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