Run the simulation for the case

Assignment Help Other Subject
Reference no: EM131223986

Homework - Reliable Intuition?

Consider a renewal process. Let X be the inter renewal times; and let I and R be the length of an interval interrupted at random and its remainder, respectively. The following BASIC simulation calculates the average values of X, I, and R (based on 10,000 replications of I and R, where T is a random interruption point).

100         FOR j=1 TO 10000

110         S=0

120         T = -1000*LOG(1-RND)

130         X=

140         c=c+1

150         SX=SX+X

160         S=S+X

170         IF S<T THEN 130

180         R=S-T: I=X

190         SR=SR+R: SI=SI+I

200         NEXT j

210         PRINT SX/c, SI/10000, SR/10000

a. Run the simulation for the case when X is exponentially distributed (that is, the renewal process is a Poisson process) with E(X) = 1.  Fill in the following table.

E(X)

E(I)

E(R)

theory

simulation

theory

simulation

theory

Simulation

 

 

 

 

 

 

Comment on the assertion:  "It is intuitively obvious that E(I) = E(X) and E(R) = E(X) / 2."

b. Let X = Y + u, where u is a constant (to be treated as a parameter), and Y is a random variable with probability distribution: P(Y=1) = 0.9, P(Y=11) = 0.1. Run the simulation and fill in the values indicated in the table. Calculate the theoretical values of E(I) and E(R) according to the formulas (to be derived later): E(I) = E(X) + V(X) / E(X) and E(R) = E(I)/2.

Draw the theoretical graph of E(R) versus u. On the same graph, plot the points produced by the simulation.

Comment on the assertion: "It is intuitively obvious that as the average length of the random interval X increases (that is, as u increases), the average lengths of the interrupted interval I and its remainder R will also increase."

 

E(X)

E(I)

E(R)

u

theory

simulation

theory

simulation

theory

simulation

0.0

 

 

 

 

 

 

0.5

 

 

 

 

 

 

1.0

 

 

 

 

 

 

1.5

 

 

 

 

 

 

2.0

 

 

 

 

 

 

2.5

 

 

 

 

 

 

3.0

 

 

 

 

 

 

3.5

 

 

 

 

 

 

4.0

 

 

 

 

 

 

4.5

 

 

 

 

 

 

5.0

 

 

 

 

 

 

Reference no: EM131223986

Questions Cloud

Cost of goods sold for lambda corporation : Lambda Corporation has current liabilities of $430,000, a quick ratio of 1.7, inventory turnover of 4.9, and a current ratio of 3.4. What is the cost of goods sold for Lambda Corporation?
Strategies to address the concerns regarding profitability : Identify strategies to address the concerns regarding profitability, and recommends KPIs for monitoring the system going forward.
What advice do you give shawn regarding forming project team : What advice do you give Shawn regarding forming the project team? How should Shawn handle the situation where some team members possess far more experience managing these types of projects?
What value would you expect your portfolio to have : If you have a portfolio with a market value of $1,000,000 and a beta (measured against the S&P 500) of 0.7, then if the market rises by 9.6 percent, what value would you expect your portfolio to have?
Run the simulation for the case : MAP 6264 Homework - Reliable Intuition? Run the simulation for the case when X is exponentially distributed (that is, the renewal process is a Poisson process) with E(X) = 1.  Fill in the following table
What is the value of ending inventory : a. Assuming that Convex sold 20,000 units during the last six months of the year at $14 each, what would gross profit be? b. What is the value of ending inventory?
Describe a time you experienced a personality conflict : Describe a time you experienced a personality conflict, and discuss how you addressed it.
Describe the services within the health care industry : Describe the services within the health care industry. The U.S. health care system is a complex delivery system comprised of many organizations that each have a role in ensuring quality of care.
What should be the future of the us space program : What should be the future of the US Space Program? Should the US Space Program become privatized or be supported by tax dollars? Should it be discontinued completely and the money spent for programs here on Earth?

Reviews

Write a Review

 

Other Subject Questions & Answers

  What are traditional ethical theories

What are traditional ethical theories. Determine the effect of traditional ethical theories on a culture of justice.

  Biography and the sociological imagination

Did you read a book (Biography and the Sociological Imagination ) by Michael Shanahan and Ross Macmillan? Some sociologists argue that we are the product of both our own agency (that is, what we make of ourselves) and social structures (that is, wh..

  About the trait theories of personality

What did you learn about yourself from reading about the trait theories of personality?

  Security interest in bank

Sam went to Stable National Bank, borrowed $1,000, and granted a security interest in his sailboat to the bank. This security interest attached on March 1 and was perfected when the bank filed a financing statement on May 15. On April 12, Sam went to..

  Normal population with a population mean

A random sample of n = 16 scores is obtained from a normal population with a population mean equal to 40 and a population standard deviation equal to 8. What is the probability that the sample mean will be within 2 points of the population mean?

  Debates about constitutionality of laws

Research the debate about the role of courts, and specifically the Supreme Court, in deciding debates about constitutionality of laws and regulations

  Develop a wbs for the tournament

Where can Nicolette find additional information to help her develop a WBS for the tournament?

  Identity in a global society

1024x768 Normal 0 false false false EN-US X-NONE X-NONE Identity in a Gl..

  Somatoform and dissociative disorders

Topics - Dissociative Disorders, Which side of the argument of repressed memories did you find to be the most compelling

  Project justification statement

Which of the following charter elements defines the project purpose and serves as the project justification statement?

  Staffing patterns assignment

Staffing Patterns Assignment

  Relationships between learning and memory

There are four main kinds of learning and their associated forms of memory, and these are defined as well.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd