   # Vital Statistics The probability distribution of the random variable x , the number of children per family in a city, is shown in the table. Find the expected value, variance, and standard deviation of x . x 0 1 2 3 4 P ( x ) 0.12 0.31 0.43 0.12 0.02 ### 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 20RE
Textbook Problem
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## Vital Statistics The probability distribution of the random variable x, the number of children per family in a city, is shown in the table. Find the expected value, variance, and standard deviation of x. x 0 1 2 3 4 P(x) 0.12 0.31 0.43 0.12 0.02

To determine

To calculate: The expected value, variance and standard deviation of the probability distribution of the random variable x which represents the number of children per family in a city.

 x 0 1 2 3 4 P(x) 0.12 0.31 0.43 0.12 0.02

### Explanation of Solution

Given Information:

The probability distribution of the random variable x which represents the number of children per family in a city is:

 x 0 1 2 3 4 P(x) 0.12 0.31 0.43 0.12 0.02

Formula used:

If a discrete random variable takes the values {x1,x2,,xm}, then the expected value of the random variable is defined as,

E(x)=x1P(x1)+x2P(x2)++xmP(xm)

Variance of the random variable is defined as,

V(x)=(x1μ)2P(x1)+(x2μ)2P(x2)++(xmμ)2P(xm)

The standard deviation of the random variable is defined as,

σ=V(x)

Calculation:

Consider the provided probability distribution of the number of children per family in a city.

 x 0 1 2 3 4 P(x) 0.12 0.31 0.43 0.12 0.02

First use the provided probability distribution and the expected value formula E(x)=x1P(x1)+x2P(x2)++xmP(xm) to calculate the expected value of the probability distribution.

So, the expected value is calculated as,

E(x)=(0)(0

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