Question 10978 – GATE 2005-IT
December 5, 2023Question 873 – Engineering-Mathematics
December 6, 2023Question 846 – Engineering-Mathematics
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
Correct Answer: D
Question 643 Explanation:
→ In probability theory, a Poisson process is a stochastic process that counts the number of events and the time points at which these events occur in a given time interval.
→ The time between each pair of consecutive events has an exponential distribution with parameter λ and each of these inter-arrival times is assumed to be independent of other inter-arrival times.
→ λ = (40*30)/60
= 20
P(T > 40min) = 1 – P(T ≤ 40 min)
= 1 – (1 – e-40min/λ)
= 1 – (1 – e-40min/20)
= e-20
→ The time between each pair of consecutive events has an exponential distribution with parameter λ and each of these inter-arrival times is assumed to be independent of other inter-arrival times.
→ λ = (40*30)/60
= 20
P(T > 40min) = 1 – P(T ≤ 40 min)
= 1 – (1 – e-40min/λ)
= 1 – (1 – e-40min/20)
= e-20
e-15
1 – e-15
1 – e-20
e-20
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