K 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. C. No, the random variable x is categorical instead of numerical. X P(x) 0 0.034 0.146 1 2 3 4 5 0.320 0.320 0.146 0.034 D. No, the random variable x's number values are not associated with probabilities. E. No, the sum of all the probabilities is not equal to 1. A. H=1 child(ren) (Round to one decimal place as needed.) B. The table does not show a probability distribution. 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.
K 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. C. No, the random variable x is categorical instead of numerical. X P(x) 0 0.034 0.146 1 2 3 4 5 0.320 0.320 0.146 0.034 D. No, the random variable x's number values are not associated with probabilities. E. No, the sum of all the probabilities is not equal to 1. A. H=1 child(ren) (Round to one decimal place as needed.) B. The table does not show a probability distribution. 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.
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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![**Transcription for Educational Website - Understanding Probability Distributions**
---
**Scenario:**
Five males with an X-linked genetic disorder have one child each. The random variable \(x\) represents 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:**
| \(x\) | \(P(x)\) |
|-------|-----------|
| 0 | 0.034 |
| 1 | 0.146 |
| 2 | 0.320 |
| 3 | 0.320 |
| 4 | 0.146 |
| 5 | 0.034 |
---
**Questions and Analysis:**
**Does the table show a probability distribution? Select all that apply.**
- [x] A. Yes, the table shows a probability distribution.
- [ ] B. No, not every probability is between 0 and 1 inclusive.
- [ ] C. No, the random variable \(x\) is categorical instead of numerical.
- [ ] D. No, the random variable \(x\)'s number values are not associated with probabilities.
- [ ] E. No, the sum of all the probabilities is not equal to 1.
**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.**
- [x] A. \(\mu = 1\) child(ren) (Round to one decimal place as needed.)
- [ ] B. The table does not show a probability distribution.
---
**Explanation:**
The table represents a probability distribution as it fulfills the criteria:
1. Each probability \(P(x)\) is between 0 and 1 inclusive.
2. The random variable \(x\) is numerical.
3. The sum of all probabilities equals 1 (\(0.034 + 0.146 + 0.320 + 0.320 + 0.146 + 0.034 = 1\)).
The mean of the distribution, calculated as \(\mu = \sum [x \cdot P(x)]\), results in 1 child, indicating the expected number](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c582252-6541-4096-9706-b4f3b52fcf1c%2Fc7e19151-066d-490c-82ff-ce7c572237ac%2F1bpdame_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website - Understanding Probability Distributions**
---
**Scenario:**
Five males with an X-linked genetic disorder have one child each. The random variable \(x\) represents 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:**
| \(x\) | \(P(x)\) |
|-------|-----------|
| 0 | 0.034 |
| 1 | 0.146 |
| 2 | 0.320 |
| 3 | 0.320 |
| 4 | 0.146 |
| 5 | 0.034 |
---
**Questions and Analysis:**
**Does the table show a probability distribution? Select all that apply.**
- [x] A. Yes, the table shows a probability distribution.
- [ ] B. No, not every probability is between 0 and 1 inclusive.
- [ ] C. No, the random variable \(x\) is categorical instead of numerical.
- [ ] D. No, the random variable \(x\)'s number values are not associated with probabilities.
- [ ] E. No, the sum of all the probabilities is not equal to 1.
**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.**
- [x] A. \(\mu = 1\) child(ren) (Round to one decimal place as needed.)
- [ ] B. The table does not show a probability distribution.
---
**Explanation:**
The table represents a probability distribution as it fulfills the criteria:
1. Each probability \(P(x)\) is between 0 and 1 inclusive.
2. The random variable \(x\) is numerical.
3. The sum of all probabilities equals 1 (\(0.034 + 0.146 + 0.320 + 0.320 + 0.146 + 0.034 = 1\)).
The mean of the distribution, calculated as \(\mu = \sum [x \cdot P(x)]\), results in 1 child, indicating the expected number
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