Define System. Write the components of a system with an example.

 Explain the characteristics of a System.

Define the following terms with example:

i) Open System

ii) Closed System

At a grocery store with one counter, customers arrive at random from 1 to 8 minutes apart (each of inter-arrival time has the same probability of occurrence). The service times vary from 1 to 6 minutes with the probabilities as 0.10, 0.20, 0.30, 0.25, 0.10 and 0.05 respectively. Analyze the system by simulating the arrival and service of 15 customers. [Justifying your situation and requirements, you can choose your required random values]

Write short notes on the followings:

i) Weibull Distribution

ii) Gamma Distribution

iii) Geometric Distribution

iv) Bernoulli Distribution

A Hurricane is to hit in the country, and expected to follow poisson distribution with a mean of 0.8 per year. Find the possibility of occurring more than two hurricanes in a year. Also find the possibility of exactly one hurricane in a year.

Explain over aspects and characteristics of a Queueing System.

 Customers at a restaurant arrive in groups (one to eight persons). The number of persons (per group) for 300 customers and the relative frequencies appear are shown below. Draw empirical CDF.

Explain different methods of random number generation.

 What are the challenges in generating pseudo random numbers.

 When Linear Congruential Generator is used?

 How Linear Congruential Generator is implemented? Explain with an example.

 Explain two methods of uniformity test with appropriate examples.

Suppose that x and y are jointly discrete random variables with

Are x and y independent?

Suppose that x and y are jointly continuous random variables with

Compute E(x), Var(x), E(y), Var(y), Cov(x, y), Cor(x, y)

 Test for whether the 3rd, 8th, 13th, and so on, numbers in the following sequence at the beginning of this section are autocorrelated using a = 0.05.

 Explain how simulation and modelling can play an important role in Manufacturing and Material Handling System.

Briefly describe probable simulation processes in a Manufacturing System [Use an appropriate example].

 Define verification in simulation process? Describe techniques to perform verification on simulation model.