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Chapter 3: Q4E (page 95)

Let X = the number of nonzero digits in a randomly selected 4-digit PIN that has no restriction on the digits. What are the possible values of X? Give three possible outcomes and their associated X values.

Short Answer

Expert verified

The possible values of X are:

\(X = \left\{ \begin{array}{l}0,\,\,\,{\rm{if all digits are zero}}\\1,\,\,\,\,{\rm{if three digits are zero}}\\2,\,\,\,{\rm{if two digits are zero}}\\3,\,\,\,{\rm{if one digit is zero}}\\4,\,{\rm{if}}\,{\rm{all digits are non - zero}}\end{array} \right.\)

The three possible outcomes and their associated X values are:

4-digit PIN

X

3123

4

4780

3

1000

1

Step by step solution

01

Given information

A random variable X is defined as the number of non-zero digits in a randomly selected PIN that has 4 numbers either zero or non-zero.

02

Determine the possible values of X

There are four places in a 4-digit PIN in which either zero or non-zero digits can be placed.

So, the minimum possible value of the random variable is 0 and the maximum possible value is 4.

The random variable X is defined by,

\(X = \left\{ \begin{array}{l}0,\,\,\,{\rm{if all digits are zero}}\\1,\,\,\,\,{\rm{if three digits are zero}}\\2,\,\,\,{\rm{if two digits are zero}}\\3,\,\,\,{\rm{if one digit is zero}}\\4,\,{\rm{if}}\,{\rm{all digits are non - zero}}\end{array} \right.\)

03

List three possible outcomes with their associated values of X

Suppose three 4-digit PIN are selected randomly, and then the possible outcomes are 3123, 4780 and 1000.

Following table represent the possible outcomes and their associated values of X which represent the number of non-zero digits in 4-digit PIN.

4-digit PIN

X

3123

4

4780

3

1000

1

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