1. Overview Mathematical visualization has a long history in mathematics and is
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Question
1. Overview Mathematical visualization has a long history in mathematics and is one of the most important application areas of visualization. Mathematical visualization utilizes 2D or 3D drawings, animations, and interactive user interfaces for understanding and exploring mathematical relationships among different obects. In this programming assignment you will generate visualizations of two types of mathematical entities: theoretical probability density functions and histograms of existing input data. Both visualizations are used to perform input analysis, one critical and often the first step in many simulation applications A simulation can be considered as a black box for generating some outputs based orn some inputs. For example, to simulate and improve the operations of a banking center the inputs can be the time between customer arrivals and the customer service time, and the outputs can be the average customer waiting time and the average number of customers in the waiting line. Usually real data are collected for inputs and are analyzed for fitting a probability distribution to them. For example, exponential distribution is a very good representation of the time between customer arrivals. A histogram is a graphical representation of the distribution of a set of data. Its generation will be discussed in detail in Section 3 Tasks. You will first generate histograms for the input data and graphical representations of theoretical probability distributions. Then you will adjust the parameters of theoretical distributions so that they match the histograms. The theoretical distribution that best matches the input histogram will be selected and used to generate input data for the simulation.Explanation / Answer
Solution:
1. Overview
Mathematical visualization has a long history in mathematics and is one of the most
important application areas of visualization. Mathematical visualization utilizes 2D or
3D drawings, animations, and interactive user interfaces for understanding and exploring
mathematical relationships among different objects. In this programming assignment,
you will generate visualizations of two types of mathematical entities: theoretical
probability density functions and histograms of existing input data. Both visualizations
are used to perform input analysis, one critical and often the first step in many simulation
applications.
A simulation can be considered as a black box for generating some outputs based on
some inputs. For example, to simulate and improve the operations of a banking center,
the inputs can be the time between customer arrivals and the customer service time, and
the outputs can be the average customer waiting time and the average number of
customers in the waiting line. Usually real data are collected for inputs and are analyzed
for fitting a probability distribution to them. For example, exponential distribution is a
very good representation of the time between customer arrivals.
A histogram is a graphical representation of the distribution of a set of data. Its
generation will be discussed in detail in Section 3 Tasks. You will first generate
histograms for the input data and graphical representations of theoretical probability
distributions. Then you will adjust the parameters of theoretical distributions so that they
match the histograms. The theoretical distribution that best matches the input histogram
will be selected and used to generate input data for the simulation.
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