The probability of digit doccurring is

Pr(d) = Log10 (1+(1/d))

where d= 1, 2, ... , 9 .

Calculate Pr(d)for d= 1, 2, ... , 9, check that the sum of all probabilities is one, and graph the probability mass function in Excel.

(a) What is the expected value of the leading digit?

(b) What is the median value of the leading digit?

(c) What is the modal value of the leading digit?

(d) What is the probability that the leading digit of a number is 3 or less? That is, find the value of the distribution function F(x) when x = 3.