Question

Consider a computer system with Poisson job arrivals stream at an average rate of 60 per hour. Determine the probability that the time interval between successive job arrivals is (i) longer than 4 minutes (ii) shorter than 8 minutes (iii) between 2 and 6 minutes.​

Answer 1

Step-by-step explanation:

Consider a computer system with Poisson job arrivals stream at an average rate of 60 per hour. Determine the probability that the time interval between successive job arrivals is (i) longer than 4 minutes (ii) shorter than 8 minutes (iii) between 2 and 6 minutes.

Answer 2

Answer:

a) 0.01831    

b) 0.9997      

c) 0.1328565

Step-by-step explanation:

Interarrivals times X are exponential with rate 60 per hour, or better for these problems λ = 1 per minute

a) P { X > 4 } = exp(-4)

                    = 0.01831

b) P { X ≤ 8 } = 1 - exp(-8)

                    = 0.9997

c) P{ 2 ≤ X ≤ 6 } = P { X ≤ 6 } - P  { X ≤ 2 }

                         = ( 1 - e⁻⁶) - ( 1 - e⁻²)                    [ ∴ e = 2.718281 ]

                         = e⁻² - e⁻⁶

                         = 0.1328565  

So , a) P { X > 4 } =  0.01831  

       b) P { X ≤ 8 } = 0.9997    

       c ) P{ 2 ≤ X ≤ 6 } = 0.1328565  

     

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