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Example 8: Triangular PDF: (X) Is Identical To The One That Would

The document describes a triangular probability distribution for the total distance traveled by emergency patients to a hospital located in the center of a 1 by 1 mile square district. The travel is parallel to the sides of the square and patient demands are uniformly distributed over the square. A relationship is noted between the random variable for total distance and other random variables that could be used to generate samples from the triangular distribution by taking the square root of the sum of the squares of two uniformly distributed random numbers.

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Jehu Amanna
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36 views1 page

Example 8: Triangular PDF: (X) Is Identical To The One That Would

The document describes a triangular probability distribution for the total distance traveled by emergency patients to a hospital located in the center of a 1 by 1 mile square district. The travel is parallel to the sides of the square and patient demands are uniformly distributed over the square. A relationship is noted between the random variable for total distance and other random variables that could be used to generate samples from the triangular distribution by taking the square root of the sum of the squares of two uniformly distributed random numbers.

Uploaded by

Jehu Amanna
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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21/11/2020 UOR_7.1.

Example 8: Triangular PDF

A hospital is located at the center of a district I- by 1-mile square.


Travel is parallel to the sides of the square, and emergency patient
demands are distributed uniformly over the square. We wish to
generate sample values of the total distance between an emergency
patient and the hospital. The pdf for the total distance D = D~ + D, is
shown in Figure 7.11.

2. If we decide to search for a relationship between random variable X


and some other random variable(s), we should be able to note
immediately that the pdf fx(x) is identical to the one that would
have resulted from the definition

where Y1 and Y2 are independent, identically distributed random


variables with uniform distributions in [0, 1). (Readers should
convince themselves that this is so.) Therefore, a very simple
method for generating random observations of X is to use

where r1 and r2 are the usual random numbers obtained through the
random-number generator. This is equivalent to generating samples
https://web.mit.edu/urban_or_book/www/book/chapter7/7.1.3.html 9/10

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