Chapter 2.1, Problem 4E

Let X be a discrete random variable with pmf $f\left(x\right)={\log }_{10}\left(\frac{x+1}{x}\right),x=1,2,\mathrm{..}.,9$.

(This distribution, known as the Benford distribution, has been shown to accurately model the probabilities of the leading signific ant digit in numbers occurring in many datasets.)

(a) Verify that f(x) satisfies the conditions of a pmf.

(b) Find the cdf of X.