Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 34 / 2 / e

Table of contents
- Solution e

Solution

The normalized log-uniform distribution here has density

1/ (x lo g 10)

. A leading digit

i

corresponds to

i \leq X < i + 1

, so

P (D = i) = \frac{1}{lo g 10} \int_{i}^{i + 1} \frac{d x}{x} = lo g_{10} (1 + 1/ i), i = 1, \dots, 9.

These are exactly the Benford law probabilities. Continuous densities make endpoint conventions immaterial.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version