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Following are results from three hypothetical corporate tax returns. Each purports to be a list of expenditures, in dollars,Here is the probability distribution of digits as predicted by Benfords law: Digit Frequency 0.301 0.176 0.125 0.097 0.079 01990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2633.66 3168.83 3301.11 3754.0Virginia 7,567,465 6,287,759 Washington West Virginia 1,816,856 Wisconsin 5,536,201 509,294 Wyoming Here is a frequency distrIndiana 6,271,973 lowa 2,966,334 Kansas 2,744,687 Kentucky 4,173,405 Louisiana 4.523,628 Maine 1,321,505 Maryland 5,600,388 MOne of the most surprising probability distributions found in practice is given by a rule known as Benfords law. This probab

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Answer #1

Solution

Back-up Theory

Benford’s Law:

In naturally occurring numbers smaller digits occur more frequently as the first digit than larger digits. Digits 1, 2 and 3 account for approximately 60 percent of the total frequency.

Now to work out the solution,

Frequency distributions of the first digit in the given three cases are given below:

First digit

Frequency

Case 1

Case 2

Case 3

1

9

4

10

2

3

4

5

3

3

2

5

4

2

3

2

5

2

4

2

6

2

3

3

7

4

5

0

8

2

2

2

9

3

3

1

Total

30

30

30

Case 1 and Case 3 follow Benford’s Law. But, Case 2 does not. So, the figures are not natural. Hence, it is reasonable to conclude that Case 2 is fraud. Answer

DONE

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