1. (25 points) Our number system consists of the digits 0, 1,2, 3,4,5,6,7, 8,9.
ID: 3329411 • Letter: 1
Question
1. (25 points) Our number system consists of the digits 0, 1,2, 3,4,5,6,7, 8,9. Because such as 12 as 012, the first significant digit in any number accounting records, tax we do not write numbers must returns, etc. We may think that each digit appears with equal frequency so that each of the nine digits has a probability of being the first digit (in other words, equally-likely outcomes), but this is not true. be 1, 2, 3, 4, 5, 6, 7, 8, 9. Consider entries of numbers in In 1881, Simon Newcomb discovered that first digits for numbers in records do not occur with equal frequency. The physicist Frank Benford discovered the same result in 1938. After studying lots and lots of data, he assigned probabilities of occurrence as shown in the table below. The probability law is now known as Benford's Lau role in identifying fraudulent data on tax returns and accounting books. Digit 6 9 Probability 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Table 1: Benford's Law (a) (5 points) Verify that Benford's Law satisfies our second probbility rule, namely AS) = 1. The numbers sn 0 ul d add to, one. Exam ple: 20 (b) (5 points) Use Benford's Taw to the determine the probability that a randomly selected entry In some accounting books has a first digit that is a 1 or a 2. = (c) (5 points) Compute the probability that a randomly selected entry in some ac- counting books has a first digit that is 1 or 2 under the assumption that the digits l are equally-likely ="11 +.11 How many more times is this event more likely under Benford's Law? more likely onder Bentords law because umbers a re coeigned deferent-IC.. 291 (d) (5 points) Use Benford's Law to determine the probability thfát a randomly selected entry in some accounting books has a first digit that is at least 6, i.e. P(X 26)Explanation / Answer
I guess you need answer to just part d and e of the question
d) P(X>=6)= 0.067+0.058+0.051+0.046 = 0.222
e)P(X<6) = 1-P(X>=6)
=0.778
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