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In a multi-user operating system, 20 requests are made to use a particular resource per hour, on an average. The probability that no requests are made in 45 minutes is
- a)e-15
- b)e-5
- c)1 - e-5
- d)1 - e-10
Correct answer is option 'A'. Can you explain this answer?
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In a multi-user operating system, 20 requests are made to use a partic...
The arrival pattern is a Poission distribution.
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In a multi-user operating system, 20 requests are made to use a partic...
Given:
- 20 requests are made to use a particular resource per hour, on an average.
- We need to find the probability that no requests are made in 45 minutes.
Approach:
- Since the average number of requests per hour is given, we can assume that the number of requests follows a Poisson distribution.
- We can use the Poisson distribution formula to find the probability of no requests in 45 minutes.
Formula:
- The Poisson distribution formula for the probability of x events occurring in a fixed time interval with an average rate of λ events per interval is:
P(x) = (e^-λ * λ^x) / x!
- Here, λ is the average rate of events per interval, and x is the number of events we want to find the probability for.
Calculation:
- We need to find the probability of no events (i.e., x = 0) in 45 minutes, which is 3/4th of an hour.
- The average rate of events per hour is given as 20.
- So, λ = 20 events per hour.
- We need to find the probability of 0 events in 3/4th of an hour.
- So, the time interval is 3/4th of an hour, and the average rate of events per interval is λ = 20 * 3/4 = 15.
- Substituting these values in the Poisson distribution formula, we get:
P(0) = (e^-15 * 15^0) / 0! = e^-15
- Therefore, the probability that no requests are made in 45 minutes is e^-15, which is approximately 3.06 * 10^-7.
Answer:
- The correct answer is option 'A' (e^-15).
- 20 requests are made to use a particular resource per hour, on an average.
- We need to find the probability that no requests are made in 45 minutes.
Approach:
- Since the average number of requests per hour is given, we can assume that the number of requests follows a Poisson distribution.
- We can use the Poisson distribution formula to find the probability of no requests in 45 minutes.
Formula:
- The Poisson distribution formula for the probability of x events occurring in a fixed time interval with an average rate of λ events per interval is:
P(x) = (e^-λ * λ^x) / x!
- Here, λ is the average rate of events per interval, and x is the number of events we want to find the probability for.
Calculation:
- We need to find the probability of no events (i.e., x = 0) in 45 minutes, which is 3/4th of an hour.
- The average rate of events per hour is given as 20.
- So, λ = 20 events per hour.
- We need to find the probability of 0 events in 3/4th of an hour.
- So, the time interval is 3/4th of an hour, and the average rate of events per interval is λ = 20 * 3/4 = 15.
- Substituting these values in the Poisson distribution formula, we get:
P(0) = (e^-15 * 15^0) / 0! = e^-15
- Therefore, the probability that no requests are made in 45 minutes is e^-15, which is approximately 3.06 * 10^-7.
Answer:
- The correct answer is option 'A' (e^-15).
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