Question

All number Passwords. The technology consultancy Data genetics published the online document PIN analysis. In addition to analyzing PIN numbers, passwords trends were examined. seven million number passwords were collected and yielded the following estimate of the probability distribution of the number of digit used in an all numeric password.

On average, approximately how many digit would expect an all numeric password to have ? Explain your answer.

Short answer

The average number of digits in an all-number password is 5.415.

Step-by-step solution

Step 1. Given information. 

Consider the following data table:

Digit	Probability	Digit	Probability
4	0.492	9	0.029
5	0.092	10	0.015
6	0.178	11	0.004
7	0.073	12	0.003
8	0.113	13	0.001

Step 2. The average number of digits an all-number password can include.

Let X be a random variable representing the number of digits in an all-digit password.

$$\begin{gathered} \mu =\sum _{}x·P(X=x) \\ \mu =1.968+0.46+1.068+0.511+0.904+0.261+0.15+0.044+0.036+0.013 \\ \mu =5.415 \end{gathered}$$

As a result, the average value = 5.415