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Asked Oct 30, 2019
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4.11. The random variable X is said to follow the distribution of Benford's Law if
(1)
P(X ilog10
1, 2, 3,...,9
i
It has been shown to be a good fit for the distribution of the first digit of many real life data values.
P(X i) 1.
a. Verify that the preceding is a probability mass function by showing that
i-1
b. Find P(X
i)
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4.11. The random variable X is said to follow the distribution of Benford's Law if (1) P(X ilog10 1, 2, 3,...,9 i It has been shown to be a good fit for the distribution of the first digit of many real life data values. P(X i) 1. a. Verify that the preceding is a probability mass function by showing that i-1 b. Find P(X i)

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Expert Answer

Step 1

It is provided that X defined as random variable, follow the distribution of Benford’s Law.

a)

To show probability mass function, prove that

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P =1

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Step 2

Proof:

L.H.S...

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P(Xi)P(X1) +P(X =2) +.. + P(x =8)+P(X=9) 2 1 +log10 2 8+1 ++ log10 8 (9+1 +1 log.0+ +...+ log10 9 (log10 2-log10 1)(log10 3-log10 2)+.. +(log10 9-log10 8)+(log,0 10 --log10 8) -log10 10-log101 =1-0 1, R.H.S Hence Proved

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