Chapter 6.2, Problem 5E

Solution

To make: A table and a histogram showing the probability distribution for the given random variable.

The table is,

W	1	2	3
Outcomes	10	90	900
$P\left(W\right)$	$\frac{1}{100}$	$\frac{9}{100}$	$\frac{9}{10}$

The histogram is,

  

Given:

N is the random variable that gives the number of digits in a random integer from 0 through 999.

Calculation:

The total integers from 0 to 999 are 1000.

The possible values of N are 1, 2, and 3.

There are 10 single digit integers (0 to 9).

There are 90 two digit integers (10 to 99).

There are 900 three digit integers (100 to 999).

Now the probabilities are,

  $\begin{array}{c}P\left(N=1\right)=\frac{10}{1000}\\ =\frac{1}{100}\\ P\left(N=2\right)=\frac{90}{1000}\\ =\frac{9}{100}\\ P\left(N=3\right)=\frac{900}{1000}\\ =\frac{9}{10}\end{array}$

Now, the table is

W	1	2	3
Outcomes	10	90	900
$P\left(W\right)$	$\frac{1}{100}$	$\frac{9}{100}$	$\frac{9}{10}$

And the histogram is,