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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.

**Given Information:**

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

**Formula used:**

If a discrete random variable takes the values

Variance of the random variable is defined as,

The standard deviation of the random variable is defined as,

**Calculation:**

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

First use the provided probability distribution and the expected value formula

So, the expected value is calculated as,

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