Frank Benford, a physicist working in the 1930s, discovered an interesting fact about some sets of numbers. While you might expect the first digits of numbers such as street addresses or checkbook entries to be randomly distributed (each with probability 1/9), Benford showed that in many cases the distribution of leading digits is not random, but rather tends to have more ones, with decreasing frequencies as the digits get larger. If a random variable X records the first digit in a street address, Benford€™s law says the probability function for X is

(a) According to Benford€™s law, what is the probability that a leading digit of a street address is 1? What is the probability for 9?
(b) Using this probability function, what proportion of street addresses begin with a digit greater than 2?

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P(X = k) = log10(1 +1/k)