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Sagot :
(a) The standard deviation is 2.582
(b) No, because the standard deviations of these two distributions are not too different from one another.
a) In this question we have been given
The given information is:
First Digit 1 2 3 4 5 6 7 8 9
Probability 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
Now we find the standard deviation.
The mean for given data is:
μ = ∑xP(X = x)
μ = (1*1/9) +(2*1/9)+(3*1/9)+(4*1/9)+(5*1/9)+(6*1/9)+(7*1/9)+(8*1/9)+(9*1/9)
μ = 5
The standard deviation is:
σ² = ∑(x - μ)²P(X)
σ² = (1 - 5)² *1/9 +(2 - 5)²*1/9+(3 - 5)²*1/9+(4 - 5)²*1/9 + (5 - 5)²*1/9+(6 - 5)²*1/9+(7-5)²*1/9+(8-5)²*1/9)+(9-5)²*1/9
σ² = 2.582
(b) The uniform distribution's standard deviation is 2.582, while Benford's law's standard deviation is 2.46
Using the standard deviation to detect fraud is not a good idea because the two distributions have about the same standard deviation
Therefore, (a) The standard deviation is 2.582
(b) using standard deviations would not be a good way to detect fraud.
Learn more about standard deviation here:
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The complete question is:
Benford’s law and fraud
(a) Using the graph from Exercise 21, calculate the standard deviation σY. This gives us an idea of how much variation we’d expect in the employee’s expense records if he assumed that first digits from 1 to 9 were equally likely.
(b) The standard deviation of the first digits of randomly selected expense amounts that follow Benford’s law is . Would using standard deviations be a good way to detect fraud? Explain your answer.
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