   # Bar Code Use the frequency distribution in Exercise 5 to find the probability distribution for the random variable. Bar Code A computer randomly selects a three-digit bar code. Each digit can be 0 or 1, and x is the number of 1’s in the bar code. x 0 1 2 3 n ( x ) ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 7RE
Textbook Problem
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## Bar Code Use the frequency distribution in Exercise 5 to find the probability distribution for the random variable.Bar Code A computer randomly selects a three-digit bar code. Each digit can be 0 or 1, and x is the number of 1’s in the bar code. x 0 1 2 3 n(x)

To determine

To calculate: The probability distribution of the random variable x which is defined as the number of 1’s in the three-digit bar code with each digit being 0 or 1 using the frequency distribution.

### Explanation of Solution

Given Information:

A three-digit bar code is randomly selected by a computer with each digit can be 0 or 1. The random variable x is defined as the number of 1’s in the bar code.

Formula used:

The probability of a random variable x is defined as,

P(x)=n(x)n(S)

Here, n(x) is the frequency of x and n(S) is the number of outcomes in S.

Calculation:

Consider that a three-digit bar code is randomly selected by a computer with each digit can be 0 or 1.

Define the random variable x as the number of 1’s in the bar code.

For a three-digit bar code selected randomly by a computer with digit as either 0 or 1, there will be 7 possible outcomes for the three-digit bar code. So, the sample space is:

S={000,001,010,011,100,101,110,111}

Thus, the sample space is S={000,001,010,011,100,101,110,111}.

As the random variable x is defined as the number of 1’s in the bar code, the possible values of number of occurrence of 1’s in all the outcomes are 0,1,2,3.

To find the frequencies, count the number of occurrence of 1’s in all the outcomes in the sample space.

For x=0, that is no 1’s in the bar code, the number of outcomes without the digit 1 is one.

For x=1, the number of outcomes with digit 1 occurring once is three.

For x=2, the number of outcomes with digit 1 occurring twice is three.

For x=3, the number of outcomes with digit 1 occurring thrice is one

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