who has four children. Its probability distribution is shown below. Complete parts a through c. 0 1 4 0 P(X=x) 0.0857 2 0.3208 3 0.2415 0.2447 0.1073 a. Find and interpret the mean of the random variable. p= (Round to four decimal places as needed.) View an example Help me solve this FEE 80 F4 O Get more help. F5 MacBook Air F6 F7 DII FB Clear all F9 Check answer F10
who has four children. Its probability distribution is shown below. Complete parts a through c. 0 1 4 0 P(X=x) 0.0857 2 0.3208 3 0.2415 0.2447 0.1073 a. Find and interpret the mean of the random variable. p= (Round to four decimal places as needed.) View an example Help me solve this FEE 80 F4 O Get more help. F5 MacBook Air F6 F7 DII FB Clear all F9 Check answer F10
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Probabilistic Analysis of Gender Distribution in a Small Town**
A census collected data on everyone that lived in a certain small town. The random variable \( X \) is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c.
| \( x \) | 0 | 1 | 2 | 3 | 4 |
|:-------:|:-----:|:------:|:-----:|:-----:|:-----:|
| \( P(X = x) \) | 0.0857 | 0.2447 | 0.3208 | 0.2415 | 0.1073 |
**a. Find and interpret the mean of the random variable.**
\[ \mu = \quad \] (Round to four decimal places as needed.)
*To solve for the mean \( \mu \) of the random variable, multiply each value of \( x \) by its corresponding probability \( P(X = x) \) and sum all these products.*
\[ \mu = \sum (x \cdot P(X = x)) \]
The table provided offers the probability \( P \) of each count \( x \) of girls in a four-child family. The calculation will yield the expected number of girls per family in this town.
*Note: Make sure to include all computed values in each step when performing your calculation for accuracy.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02ebb731-29eb-4cd6-ba2a-cc2ff28bf3c8%2Fcb05e409-2218-44c1-a578-d4619cae061a%2Fum7tz8k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probabilistic Analysis of Gender Distribution in a Small Town**
A census collected data on everyone that lived in a certain small town. The random variable \( X \) is the number of girls born to a randomly selected couple in that town who has four children. Its probability distribution is shown below. Complete parts a through c.
| \( x \) | 0 | 1 | 2 | 3 | 4 |
|:-------:|:-----:|:------:|:-----:|:-----:|:-----:|
| \( P(X = x) \) | 0.0857 | 0.2447 | 0.3208 | 0.2415 | 0.1073 |
**a. Find and interpret the mean of the random variable.**
\[ \mu = \quad \] (Round to four decimal places as needed.)
*To solve for the mean \( \mu \) of the random variable, multiply each value of \( x \) by its corresponding probability \( P(X = x) \) and sum all these products.*
\[ \mu = \sum (x \cdot P(X = x)) \]
The table provided offers the probability \( P \) of each count \( x \) of girls in a four-child family. The calculation will yield the expected number of girls per family in this town.
*Note: Make sure to include all computed values in each step when performing your calculation for accuracy.*
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