Faked numbers in tax returns, invoices, or expense account claims often display patterns that are not present in legitimate records. Some patterns like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can't be 0). E(X) = 3.441. First digit x; Probability Pi 1 0.301 2 0.176 3 0.125 What is the standard deviation of X? Interpret this value. 4 0.097 5 0.079 6 0.067 7 0.058 8 0.051 9 0.046 x = 2.462. The first digit of a randomly chosen record will typically vary from 2.462 by about 3.441. ox= 6.0605. The first digit of a randomly chosen record will typically vary from the mean (3.441) by about 6.0605. ox=6.0605. The first digit of a randomly chosen record will typically vary from 6.0605 by about 3.441. ox=2.462. The first digit of a randomly chosen record will typically vary from the mean (3.441) by about 2.462. The standard deviation cannot be calculated in this situation because we do not have a list of randomly selected first digits.
Faked numbers in tax returns, invoices, or expense account claims often display patterns that are not present in legitimate records. Some patterns like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle. It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can't be 0). E(X) = 3.441. First digit x; Probability Pi 1 0.301 2 0.176 3 0.125 What is the standard deviation of X? Interpret this value. 4 0.097 5 0.079 6 0.067 7 0.058 8 0.051 9 0.046 x = 2.462. The first digit of a randomly chosen record will typically vary from 2.462 by about 3.441. ox= 6.0605. The first digit of a randomly chosen record will typically vary from the mean (3.441) by about 6.0605. ox=6.0605. The first digit of a randomly chosen record will typically vary from 6.0605 by about 3.441. ox=2.462. The first digit of a randomly chosen record will typically vary from the mean (3.441) by about 2.462. The standard deviation cannot be calculated in this situation because we do not have a list of randomly selected first digits.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Faked numbers in tax returns, invoices, or expense account claims often display patterns that are not present in legitimate
records. Some patterns like too many round numbers, are obvious and easily avoided by a clever crook. Others are more subtle.
It is a striking fact that the first digits of numbers in legitimate records often follow a model known as Benford's law. Call the
first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first
digit can't be 0). E(X) = 3.441.
First digit x;
Probability Pi
1
0.301
2
0.176
3
0.125
What is the standard deviation of X? Interpret this value.
4
0.097
5
0.079
6
0.067
7
0.058
8
0.051
9
0.046
ox=2.462. The first digit of a randomly chosen record will typically vary from 2.462 by about 3.441.
ox= 6.0605. The first digit of a randomly chosen record will typically vary from the mean (3.441) by about 6.0605.
ox= 6.0605. The first digit of a randomly chosen record will typically vary from 6.0605 by about 3.441.
x = 2.462. The first digit of a randomly chosen record will typically vary from the mean (3.441) by about 2.462.
The standard deviation cannot be calculated in this situation because we do not have a list of randomly selected first
digits.
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