MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Probability Distribution: X-linked Genetic Disorder

#### Problem Description
Five males with an X-linked genetic disorder each have one child. The random variable \( x \) represents the number of children, among the five, who inherit the disorder. Determine if the table represents a probability distribution, and if so, calculate the mean and standard deviation. If not, identify the failed requirements.

#### Data Table
| \( x \) | \( P(x) \) |
|--------|------------|
| 0      | 0.032      |
| 1      | 0.146      |
| 2      | 0.322      |
| 3      | 0.322      |
| 4      | 0.146      |
| 5      | 0.032      |

#### Questions
1. **Does the table show a probability distribution?** Select all that apply:
   - [ ] A. Yes, the table shows a probability distribution.
   - [ ] B. No, the random variable \( x \)'s numbers are not associated with probabilities.
   - [ ] C. No, not every probability is between 0 and 1 inclusive.
   - [ ] D. No, the random variable \( x \) is categorical instead of numerical.
   - [ ] E. No, the sum of all probabilities is not equal to 1.

2. **Find the mean of the random variable \( x \):**
   - [ ] A. \(\mu =\) _______ child(ren) (Round to one decimal place as needed.)
   - [ ] B. The table does not show a probability distribution.

3. **Find the standard deviation of the random variable \( x \):**
   - [ ] A. \(\sigma =\) _______ child(ren) (Round to one decimal place as needed.)
   - [ ] B. The table does not show a probability distribution.

#### Analyzing the Distribution

- **Probability Criteria:**
  - Each probability should be between 0 and 1.
  - The sum of all probabilities should be equal to 1.

- **Mean (\(\mu\)):**
  The mean (\(\mu\)) of a probability distribution is calculated as:
  \[
  \mu = \sum [x \times P(x)]
  \]

- **Standard Deviation (\(\sigma\)):**
  The standard deviation (\(\sigma
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Transcribed Image Text:### Probability Distribution: X-linked Genetic Disorder #### Problem Description Five males with an X-linked genetic disorder each have one child. The random variable \( x \) represents the number of children, among the five, who inherit the disorder. Determine if the table represents a probability distribution, and if so, calculate the mean and standard deviation. If not, identify the failed requirements. #### Data Table | \( x \) | \( P(x) \) | |--------|------------| | 0 | 0.032 | | 1 | 0.146 | | 2 | 0.322 | | 3 | 0.322 | | 4 | 0.146 | | 5 | 0.032 | #### Questions 1. **Does the table show a probability distribution?** Select all that apply: - [ ] A. Yes, the table shows a probability distribution. - [ ] B. No, the random variable \( x \)'s numbers are not associated with probabilities. - [ ] C. No, not every probability is between 0 and 1 inclusive. - [ ] D. No, the random variable \( x \) is categorical instead of numerical. - [ ] E. No, the sum of all probabilities is not equal to 1. 2. **Find the mean of the random variable \( x \):** - [ ] A. \(\mu =\) _______ child(ren) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. 3. **Find the standard deviation of the random variable \( x \):** - [ ] A. \(\sigma =\) _______ child(ren) (Round to one decimal place as needed.) - [ ] B. The table does not show a probability distribution. #### Analyzing the Distribution - **Probability Criteria:** - Each probability should be between 0 and 1. - The sum of all probabilities should be equal to 1. - **Mean (\(\mu\)):** The mean (\(\mu\)) of a probability distribution is calculated as: \[ \mu = \sum [x \times P(x)] \] - **Standard Deviation (\(\sigma\)):** The standard deviation (\(\sigma
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