CSM Assignment No. 2

ASSIGNMENT NO. 2

1.      The probability of a computer chip failure is 0.05. Everyday a random sample of size 14 is taken. What is the probability that 1) at most 3 will fail 2) at least 3 will fail

2.      The number of accidents in a year to taxi driver follows poisson distribution with mean equal to 3. Out of 100 taxi drivers, find approximately the number of drivers with 1) no accidents in a year 2) more than 3 accidents in a year.

3.      Explain Poisson processes with properties.

4.      Explain discrete distributions.

5.      At service station an automatic carwash facility operates with only one car bay. Cars arriving according to a position distribution, with mean of 12 cars per hour. Car may wait in the facilities parking lawn if service station is busy. Service time has distribution with average 4 min with a standard deviation of 4/3 minutes. Compute the steady state parameters of the system.

6.      The inter arrival time as well as service time at government hospital is known to be distributed exponentially. Currently only 1 emergency case can be handle at time .The arrival rate of patient is 4 per hour and service rate 6 per hour. Compute the steady state parameter and probability for 0, 1, 2, 3, 4 or more patients in the hospital.

7.      A CNG station has 2 filling machine. The service time follows exponential distribution with the mean of 5 min and autorikshaws arrives for service in a poisson fashion at a rate of 15 per hour. Compute steady state parameters of the system.