5. Suppose that you are reading through back-issues of the New York Times and record every number that appears in the articles (someone's salary, the cost of the new drones bought by the government, the number of refugees on the border, etc.). Let X be the leading digit of a randomly selected number from the articles (so X takes values between 1 and 9). Surprisingly, empirical evidence suggests that X is not uniformly distributed, but instead follows a distribution called Benford's law: p(z) = P(1st digit is 2) = log10 (). (a) Compute the probabilities for each particular leading digit, and compare this distribution to the corresponding uniform distribution. (b) Calculate the cumulative distribution function for X. (c) Using the cdf, what is the probability that the leading digit is at most 3? At least 5?

5. Suppose that you are reading through back-issues of the New York Times and record every number that appears in the articles (someone's salary, the cost of the new drones bought by the government, the number of refugees on the border, etc.). Let X be the leading digit of a randomly selected number from the articles (so X takes values between 1 and 9). Surprisingly, empirical evidence suggests that X is not uniformly distributed, but instead follows a distribution called Benford's law: p(z) = P(1st digit is 2) = log10 (). (a) Compute the probabilities for each particular leading digit, and compare this distribution to the corresponding uniform distribution. (b) Calculate the cumulative distribution function for X. (c) Using the cdf, what is the probability that the leading digit is at most 3? At least 5?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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