Question: Benford's law and fraud A not-so-clever employee decided to fake his monthly expense report. He believed that the first digits of his expense amounts should be equally likely to be any of the numbers from 1 to 9. In that case, the first digit Y of a randomly selected expense amount would have the probability distribution shown in the histogram.
(a) Explain why the mean of the random variable Y is located at the solid red line in the figure.
(b) The first digits of randomly selected expense amounts actually follow Benford's law. According to Benford's law, what's the expected value of the first digit? Explain how this information could be used to detect a fake expense report.
(c) What's P(Y > 6) in the above distribution? According to Benford's law, what proportion of first digits in the employee's expense amounts should be greater than 6? How could this information be used to detect a fake expense report?