To assign probabilities in a discrete model list the

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Unformatted text preview: 16 Chapter 10 Dr. Berg Example (10.7) Benford's Law Faked numbers in tax returns, invoices, or expense account claims often display patterns that aren't 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 record X for short. Benford's law gives this probability distribution for X: X 1 2 3 4 5 6 7 8 9 Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Investigators can detect possible fraud by comparing the first digits in records such as invoices paid by a business with these probabilities. The probability that a first digit is greater than or equal to 6 is P(X 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.067 + 0.058 + 0.051+ 0.046 = 0.222 which is less than the probability that the leading digit is 1. Fraudulent records tend to have too few 1s and too many higher first digits. Exercise (10.11) Benford's Law The first digit of a r...
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