Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in the table. 1 2 3 4 5 6. 7 8 P(x) 0.301 |0.176 | 0.125 | 0.097 | 0.079 | 0.067 | 0.058 | 0.051 | 0.046 Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that behaves according to Benford's law? Please give your answer to the nearest three decimal places.

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Benford's law, also known as the first-digit law, represents a probability distribution of the leading significant digits of
numerical values in a data set. A leading significant digit is the first occurring non-zero integer in a number. For example,
the leading significant digit in the number 127 is 1. Let this leading significant digit be denoted x.
Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in
the table.
1
3
4
5
7
8
9.
P(x) 0.301 | 0.176 | 0.125 | 0.097 0.079 | 0.067 0.058 0.051 | 0.046
Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that
behaves according to Benford's law? Please give your answer to the nearest three decimal places.
Transcribed Image Text:Benford's law, also known as the first-digit law, represents a probability distribution of the leading significant digits of numerical values in a data set. A leading significant digit is the first occurring non-zero integer in a number. For example, the leading significant digit in the number 127 is 1. Let this leading significant digit be denoted x. Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in the table. 1 3 4 5 7 8 9. P(x) 0.301 | 0.176 | 0.125 | 0.097 0.079 | 0.067 0.058 0.051 | 0.046 Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that behaves according to Benford's law? Please give your answer to the nearest three decimal places.
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