Briefly explain the differences between discrete system and continuous system with suitable figure.

Briefly explain the differences between discrete system and continuous system with suitable figure.

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.

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.

Write down the name of several entities, attributes, activities, events, and state variables for the following system i) A small appliance repair shop ii) A hospital emergency room

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

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

Explain over aspects and characteristics of a Queueing System.

Explain different methods of random number generation.

 When Linear Congruential Generator is used?

Suppose that x and y are jointly discrete random variables with

Are x and y independent?

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

What is computer simulation?

Write short notes on the followings including their scope of implementation in simulation process:

i) Exponential Distribution

iii) Lognormal Distribution

ii) Triangular Distribution

iv) Poisson Process

Define the following queuing system characteristics:

(i) Calling population

(ii) Arrival process

 What are the problems may occur during the generation of random numbers?

For the following multiplicative generator, compute Zi for enough values of i>=1 to cover an entire cycle

i) Zo1, a=11, m=16

ii) Zo2, a=11, m=16

iii) Zo 1, a2, m=13

iv) Zo2, a=3, m=13

Suppose that x and y are jointly discrete random variables with

P(x,y)=(x+y)/30     for x=0,1,2 and y=0,1,2,3

         = 0                0, therewise

Are x and y independent?

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

 Explain the characteristics of a System.

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.

 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.

 What are the challenges in generating pseudo random numbers.

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

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)

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

 Briefly describe the steps of simulation study.

b) 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.

A classical inventory problem concerns the purchase and sale of newspapers. The paper seller buys the papers for 33 cents each and sells them for 50 cents each. (The lost profit from excess demand is 17 cents for each paper demanded that could not be provided.) Newspapers not sold at the end of the day are sold as scrap for 5 cents each. (the salvage value of scrap papers). There are three types of Newsday's, "good, "fair," and "poor," with probabilities of 0.35, 0.45, and 0.20, Respectively. The problem is to determine the optimal number of papers the newspaper seller should purchase. This will be accomplished by simulating demands for 20 days and recording profits from sales each day. The demand table and distribution of type of Newsday are given below.

Simulate for the purchase of 70 newspapers per day for 20 days and compute the profit of news dealer. Random numbers for Type of News day: 94, 77, 49, 45, 43, 32, 49, 00, 16, 24, 31, 14, 41, 61, 85, 08, 15, 97, 52, 78

Random numbers for Demand: 80, 20, 15, 88, 98, 65, 86, 73, 24, 60, 60, 29, 18, 90, 93, 73, 21, 45, 76, 96

 Define linear congruential method for generating random number. Use the linear congruential method to generate a sequence of four (4) random numbers with X₀ = 27, a = 17, c = 43, and m = 100.

 Find first three random variables in [0,1] using Xo = 27, a = 8, c = 47, m = 100.

Suppose that x and y are jointly continuous random variables with

f(x,y)= y-x = 0 , for 0<x<1 and 1<y<2

          =0             otherwise

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

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

Define the following terms with example:

i) Open System

ii) Closed System

 Explain two methods of uniformity test with appropriate examples.

 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.

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

 Briefly explain the differences between discrete system and continuous system with suitable figure.

 The sequence of numbers 0.54, 0.73, 0.98, 0.11 and 0.68 has been generated. Use the Kolmogorov-Smirnov test with a = 0.05 to check uniformity.

 What are the methods are used for testing a random number? Suppose, five numbers 0.44, 0.81, 0.14, 0.05, 0.93 are generated. Test the uniformity of the generated numbers using the Kolmogorov-Smirnov test with the level of significance α = 0.05. [Critical value D_α=0.565]

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

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

 Write down the name of several entities, attributes, activities, events, and state variables for the following system i) A small appliance repair shop ii) A hospital emergency room