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As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: PT=nPy Where Pr is the total profit, n is the number of vehicles sold and P, is the profit per vehicle. PART A Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P, follows a normal distribution with a mean of $8125 and a standard deviation of $1275 Number of bins: 10 i.) ii.) PROBLEM-SOLVING EXERCISE #4 Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I'd give you a break Ⓒ. SIMULATION Parameter n Py PT Bin # $ Range iii.) 1: 6: What are the ranges for the 10 bins? Fill in the table below: Iteration 1 6 $8000 Iteration 2 8 $9100 Iteration 3 2 $2175 Fill in the frequency of occurrences of each bin: 2: 7: 3: 8: 4: 9: Iteration 4 5 $7875 Iteration 5 7 $3175 5: 10:

As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: PT=nPy Where Pr is the total profit, n is the number of vehicles sold and P, is the profit per vehicle. PART A Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P, follows a normal distribution with a mean of $8125 and a standard deviation of $1275 Number of bins: 10 i.) ii.) PROBLEM-SOLVING EXERCISE #4 Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I'd give you a break Ⓒ. SIMULATION Parameter n Py PT Bin # $ Range iii.) 1: 6: What are the ranges for the 10 bins? Fill in the table below: Iteration 1 6 $8000 Iteration 2 8 $9100 Iteration 3 2 $2175 Fill in the frequency of occurrences of each bin: 2: 7: 3: 8: 4: 9: Iteration 4 5 $7875 Iteration 5 7 $3175 5: 10:

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: PT=nPv Where Pr is the total profit, n is the number of vehicles sold and P, is the profit per vehicle. PART A Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P, follows a normal distribution with a mean of $8125 and a standard deviation of $1275 Number of bins: 10 i.) ii.) Parameter Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I'd give you a break Ⓒ. n Py PROBLEM-SOLVING EXERCISE #4 PT Bin # $ Range SIMULATION iii.) 1: 6: Iteration 1 What are the ranges for the 10 bins? Fill in the table below: $8000 Iteration 2 8 $9100 Iteration 3 $2175 Fill in the frequency of occurrences of each bin: 2: 3: 7: 8: 4: 9: Iteration 4 $7875 5: Iteration 5 7 $3175 10:
Transcribed Image Text:As we've previously seen, equations describing situations often contain uncertain parameters, that is, parameters that aren't necessarily a single value but instead are associated with a probability distribution function. When more than one of the variables is unknown, the outcome is difficult to visualize. A common way to overcome this difficulty is to simulate the scenario many times and count the number of times different ranges of outcomes occur. One such popular simulation is called a Monte Carlo Simulation. In this problem-solving exercise you will develop a program that will perform a Monte Carlo simulation on a simple profit function. Consider the following total profit function: PT=nPv Where Pr is the total profit, n is the number of vehicles sold and P, is the profit per vehicle. PART A Compute 5 iterations of a Monte Carlo simulation given the following information: n follows a uniform distribution with minimum of 1 and maximum 10 P, follows a normal distribution with a mean of $8125 and a standard deviation of $1275 Number of bins: 10 i.) ii.) Parameter Recall that for all practical purposes we will use 3 std. deviations from the mean as the maximum value for parameters following a normal distribution. Obviously, 5 iterations are not very many. In fact, typically you would simulate 10,000 iterations or so to view meaningful results but I figured that I'd give you a break Ⓒ. n Py PROBLEM-SOLVING EXERCISE #4 PT Bin # $ Range SIMULATION iii.) 1: 6: Iteration 1 What are the ranges for the 10 bins? Fill in the table below: $8000 Iteration 2 8 $9100 Iteration 3 $2175 Fill in the frequency of occurrences of each bin: 2: 3: 7: 8: 4: 9: Iteration 4 $7875 5: Iteration 5 7 $3175 10:
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PART B Write the following three methods and include in the Part D code listing: public int GetRandomUniform(int min, int max) This method returns a random number from a uniform distribution between min and max. public double GetRandomNormal(double mean, double stddev) This method returns a random number from a normal distribution with a mean of mean and standard deviation of stddev public int GetBinIndex(double mini, double maxi, int numbins, double valuetobin) This method returns the Bin Index given an input minimum of mini, input maximum of maxi, numbins number of bins, and a value to bin of valuetobin PART C Include the methods created in part B to develop a Visual C# .NET program that will simulate the basic profit calculation, PT = nPv, where n follows a uniform distribution, P, follows a normal distribution, and the user can input the number of bins and number of iterations. The user must also input the min and max for n and the mean and standard deviation for Py. Finally, the user can click a button and the results will be graphed on a bar chart using the Microsoft Chart Control and the average total profit (PT) will be displayed in a textbox. Turn in a screen shot of the resulting chart using: 1. Iterations: 10000 Bins: 5 2. Iterations: 10000 Bins: 10 3. Iterations: 10000 Bins: 10 That's three screen shots. PART D n-min: 1 n-min: 1 n-min: 1 n-max: 10 n-max: 10 n-max: 10 P-mean: 8250 Py-stddev: 1780 Py-mean: 8250 Py-stddev: 1780 P-mean: 5500 P-stddev: 1200 Extend the Visual C# .NET program developed in part C to simulate the basic profit calculation, Pr=nPv, where the user can select either a uniform or normal distribution for n using radio buttons and then must input the appropriate parameters (min and max if they select uniform, mean and standard deviation if they select normal) and they can similarly select either a uniform or normal distribution for P, with appropriate parameters depending on the selection. Of course, the user will input the number of bins and number of iterations. Finally, the user can click a button and the results will be graphed on a bar chart using the Microsoft Chart Control and the average total profit (PT) will be displayed in a textbox. Also include in the program any necessary input validation for all input values. Turn in a listing of the code and a screen shot of the resulting chart using: 1. Iterations: 10000 Bins: 5 2. Iterations: 10000 Bins: 10 n-min: 2 n-mean: 7 n- mean: 12 3. Iterations: 10000 Bins: 10 That's three screen shots and a listing of the code. n-max: 10 P-mean: 7250 n-stddev: 2 P-min: 1250 n- stddev: 3 Py-min: 2375 P-stddev: 1950 P-max: 6500 Py-max: 5450
Transcribed Image Text:PART B Write the following three methods and include in the Part D code listing: public int GetRandomUniform(int min, int max) This method returns a random number from a uniform distribution between min and max. public double GetRandomNormal(double mean, double stddev) This method returns a random number from a normal distribution with a mean of mean and standard deviation of stddev public int GetBinIndex(double mini, double maxi, int numbins, double valuetobin) This method returns the Bin Index given an input minimum of mini, input maximum of maxi, numbins number of bins, and a value to bin of valuetobin PART C Include the methods created in part B to develop a Visual C# .NET program that will simulate the basic profit calculation, PT = nPv, where n follows a uniform distribution, P, follows a normal distribution, and the user can input the number of bins and number of iterations. The user must also input the min and max for n and the mean and standard deviation for Py. Finally, the user can click a button and the results will be graphed on a bar chart using the Microsoft Chart Control and the average total profit (PT) will be displayed in a textbox. Turn in a screen shot of the resulting chart using: 1. Iterations: 10000 Bins: 5 2. Iterations: 10000 Bins: 10 3. Iterations: 10000 Bins: 10 That's three screen shots. PART D n-min: 1 n-min: 1 n-min: 1 n-max: 10 n-max: 10 n-max: 10 P-mean: 8250 Py-stddev: 1780 Py-mean: 8250 Py-stddev: 1780 P-mean: 5500 P-stddev: 1200 Extend the Visual C# .NET program developed in part C to simulate the basic profit calculation, Pr=nPv, where the user can select either a uniform or normal distribution for n using radio buttons and then must input the appropriate parameters (min and max if they select uniform, mean and standard deviation if they select normal) and they can similarly select either a uniform or normal distribution for P, with appropriate parameters depending on the selection. Of course, the user will input the number of bins and number of iterations. Finally, the user can click a button and the results will be graphed on a bar chart using the Microsoft Chart Control and the average total profit (PT) will be displayed in a textbox. Also include in the program any necessary input validation for all input values. Turn in a listing of the code and a screen shot of the resulting chart using: 1. Iterations: 10000 Bins: 5 2. Iterations: 10000 Bins: 10 n-min: 2 n-mean: 7 n- mean: 12 3. Iterations: 10000 Bins: 10 That's three screen shots and a listing of the code. n-max: 10 P-mean: 7250 n-stddev: 2 P-min: 1250 n- stddev: 3 Py-min: 2375 P-stddev: 1950 P-max: 6500 Py-max: 5450
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