91Ó°ÊÓ

The probability distribution for X is shown here

Because the highest bar in the histogram is to the left, and there is a tail of smaller bars to its right, the distribution is skewed to the right.

Because there is only one peak in the histogram, the distribution is unimodal.

Because the highest bar in the histogram is centered at 1, the most common first digit is 1.

The first digits are numbered from 1 to 9.

As a result:

Skewed to the right

Unimodal

1 is the most common first digit

The first digits range from 1 to 9

The expected value (or mean) is the sum of the product of each possibility 2, with its probability $p_i$

$$\begin{gathered} \mathrm{μ}=\underset{}{∑}{x}_i{p}_i \\ \mathrm{μ}=1x0.301+2x0.176+3x0.125+4x0.097+5x0.079 \\ +6x0.067+7x0.058+8x0.051+9x0.046 \\ \mathrm{μ}=3.441 \end{gathered}$$

The first digit of a randomly chosen legitimate record is 3.441 on average.