Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. ☐☐ A. Yes, the table shows a probability distribution. B. No, not every probability is between 0 and 1 inclusive. X 0 1 2 3 4 5 P(x) 0.029 0.152 0.319 0.319 0.152 0.029 C. No, the random variable x's number values are not associated with probabilities. D. No, the sum of all the probabilities is not equal to 1. E. No, the random variable x is categorical instead of numerical. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. μ= child(ren) (Round to one decimal place as needed.)
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Does the table show a probability distribution? Select all that apply. ☐☐ A. Yes, the table shows a probability distribution. B. No, not every probability is between 0 and 1 inclusive. X 0 1 2 3 4 5 P(x) 0.029 0.152 0.319 0.319 0.152 0.029 C. No, the random variable x's number values are not associated with probabilities. D. No, the sum of all the probabilities is not equal to 1. E. No, the random variable x is categorical instead of numerical. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. μ= child(ren) (Round to one decimal place as needed.)
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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This is a 3 part question please help!
![**Problem Statement:**
Five males with an X-linked genetic disorder have one child each. The random variable \( x \) is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
**Table Data:**
\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & 0.029 \\
1 & 0.152 \\
2 & 0.319 \\
3 & 0.319 \\
4 & 0.152 \\
5 & 0.029 \\
\hline
\end{array}
\]
**Question:**
Does the table show a probability distribution? Select all that apply.
- A. Yes, the table shows a probability distribution.
- B. No, not every probability is between 0 and 1 inclusive.
- C. No, the random variable \( x \)'s number values are not associated with probabilities.
- D. No, the sum of all the probabilities is not equal to 1.
- E. No, the random variable \( x \) is categorical instead of numerical.
**Next Step:**
Find the mean of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( \mu = \) ____ child(ren) (Round to one decimal place as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29f6c508-19b6-49d8-819e-230dd31fa335%2Ffe96cf48-97bd-41a3-99e9-5e552d353a89%2Fqbs5ias_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Five males with an X-linked genetic disorder have one child each. The random variable \( x \) is the number of children among the five who inherit the X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
**Table Data:**
\[
\begin{array}{|c|c|}
\hline
x & P(x) \\
\hline
0 & 0.029 \\
1 & 0.152 \\
2 & 0.319 \\
3 & 0.319 \\
4 & 0.152 \\
5 & 0.029 \\
\hline
\end{array}
\]
**Question:**
Does the table show a probability distribution? Select all that apply.
- A. Yes, the table shows a probability distribution.
- B. No, not every probability is between 0 and 1 inclusive.
- C. No, the random variable \( x \)'s number values are not associated with probabilities.
- D. No, the sum of all the probabilities is not equal to 1.
- E. No, the random variable \( x \) is categorical instead of numerical.
**Next Step:**
Find the mean of the random variable \( x \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- A. \( \mu = \) ____ child(ren) (Round to one decimal place as needed.)
![Here is a text transcription for an educational website:
---
### Finding the Mean and Standard Deviation of a Random Variable
**Objective:** Learn how to find the mean and standard deviation of a random variable \(x\).
---
#### Step 1: Finding the Mean of the Random Variable \(x\)
**Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** \( \mu = \) [ ] child(ren) (Round to one decimal place as needed.)
- **B.** The table does not show a probability distribution.
---
#### Step 2: Finding the Standard Deviation of the Random Variable \(x\)
**Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** \( \sigma = \) [ ] child(ren) (Round to one decimal place as needed.)
- **B.** The table does not show a probability distribution.
---
**Explanation of Terms and Concepts:**
- **Mean (\( \mu \)):** The average value of the random variable \(x\). It is calculated by taking the sum of all possible values of \(x\), each multiplied by its probability, and then summing these products.
- **Standard Deviation (\( \sigma \)):** A measure of the amount of variation or dispersion of the random variable \(x\). It is calculated by taking the square root of the variance.
- **Probability Distribution:** A table or function that shows the possible values of a random variable and their associated probabilities.
---
**Note:** The provided choices pertain to whether the given table shows a probability distribution or not, and ask the user to input the calculated values if appropriate. The user should select the option that best fits the problem at hand.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29f6c508-19b6-49d8-819e-230dd31fa335%2Ffe96cf48-97bd-41a3-99e9-5e552d353a89%2Fabt0tn1_processed.png&w=3840&q=75)
Transcribed Image Text:Here is a text transcription for an educational website:
---
### Finding the Mean and Standard Deviation of a Random Variable
**Objective:** Learn how to find the mean and standard deviation of a random variable \(x\).
---
#### Step 1: Finding the Mean of the Random Variable \(x\)
**Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** \( \mu = \) [ ] child(ren) (Round to one decimal place as needed.)
- **B.** The table does not show a probability distribution.
---
#### Step 2: Finding the Standard Deviation of the Random Variable \(x\)
**Instructions:** Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
- **A.** \( \sigma = \) [ ] child(ren) (Round to one decimal place as needed.)
- **B.** The table does not show a probability distribution.
---
**Explanation of Terms and Concepts:**
- **Mean (\( \mu \)):** The average value of the random variable \(x\). It is calculated by taking the sum of all possible values of \(x\), each multiplied by its probability, and then summing these products.
- **Standard Deviation (\( \sigma \)):** A measure of the amount of variation or dispersion of the random variable \(x\). It is calculated by taking the square root of the variance.
- **Probability Distribution:** A table or function that shows the possible values of a random variable and their associated probabilities.
---
**Note:** The provided choices pertain to whether the given table shows a probability distribution or not, and ask the user to input the calculated values if appropriate. The user should select the option that best fits the problem at hand.
---
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