UGC NET Computer Science July 2018 - II Question 53

Question 53

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53. 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 ______ .

1. (1) e^-15
2. (2) 1 - e^-15
3. (3) 1 - e^-20
4. (4) e^-20

Answer : (4) e^-20

Explanation Question 53

In 1 Hour = 30 Requests Sent
∴ In 60 minutes = 30 Requests Sent
So, in 40 minutes = (30 x 40) / 60 = 20 Requests Sent

Here 20 is Number of request Sent in 40 minutes.
Let λ is number of request in 40 minutes
∴ λ = 20

But according to given statement in question Actual requests are made in 40 minutes is ZERO.

Let x is actual requests in 40 minutes.
i.e. x = 0 (According to Question)

As arrival pattern is a poisson distribution,
So, Probablity ( x ) = ( e^-λ * λ^x ) / x !
∴ Probablity ( x = 0 ) = ( e^-20 * λ⁰ ) / 0!
∴ Probablity ( x = 0 ) = e^-20

So, option (4) is correct answer.

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