Benford's law states that in a very large variety of real-life data sets, the first digit approximately follows a particular distribution with about a 30% chance of a 1, an 18% chance of a 2 and in general p(d=j)=log10(j+1/j), for j in {1,2,}, where d is the first digit of a randomly chosen element. check that this is a valid pmf (using properties f logs, not with a calculator).