lales with an X-linked genetic disorde dom variable x is the number of children X-linked genetic disorder. Determine wh iven. If a probability distribution is given, intion If babilit ーュ

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**Title: Understanding Probability Distributions in Genetic Disorders**

**Introduction:**
In this educational section, we explore the concept of probability distributions using the example of an X-linked genetic disorder. We consider a scenario where five males with this disorder each have one child. We will determine if the given data represents a valid probability distribution and, if applicable, calculate its mean and standard deviation.

**Probability Table and Explanation:**

| x | P(x)  |
|---|-------|
| 0 | 0.031 |
| 1 | 0.158 |
| 2 | 0.311 |
| 3 | 0.311 |
| 4 | 0.158 |
| 5 | 0.031 |

- **x** represents the number of children among the five who inherit the genetic disorder.
- **P(x)** represents the probability of exactly x children inheriting the disorder.

**Analysis:**
To determine if this is a probability distribution, check the following criteria:
1. Each probability **P(x)** must be between 0 and 1 inclusive.
2. The sum of all probabilities must equal 1.

**Questions for Consideration:**
Does the table show a probability distribution? Select all that apply.

- [ ] A. Yes, the table shows a probability distribution.
- [ ] B. No, the sum of all the probabilities is not equal to 1.
- [ ] 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, not every probability is between 0 and 1 inclusive.

Examine each option and reflect on the definition of a probability distribution to decide which statements are correct.
Transcribed Image Text:**Title: Understanding Probability Distributions in Genetic Disorders** **Introduction:** In this educational section, we explore the concept of probability distributions using the example of an X-linked genetic disorder. We consider a scenario where five males with this disorder each have one child. We will determine if the given data represents a valid probability distribution and, if applicable, calculate its mean and standard deviation. **Probability Table and Explanation:** | x | P(x) | |---|-------| | 0 | 0.031 | | 1 | 0.158 | | 2 | 0.311 | | 3 | 0.311 | | 4 | 0.158 | | 5 | 0.031 | - **x** represents the number of children among the five who inherit the genetic disorder. - **P(x)** represents the probability of exactly x children inheriting the disorder. **Analysis:** To determine if this is a probability distribution, check the following criteria: 1. Each probability **P(x)** must be between 0 and 1 inclusive. 2. The sum of all probabilities must equal 1. **Questions for Consideration:** Does the table show a probability distribution? Select all that apply. - [ ] A. Yes, the table shows a probability distribution. - [ ] B. No, the sum of all the probabilities is not equal to 1. - [ ] 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, not every probability is between 0 and 1 inclusive. Examine each option and reflect on the definition of a probability distribution to decide which statements are correct.
Expert Solution
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Probability denotes the chances of occurring an event. It lies between 0 and 1. 

In the case of a probability distribution, the sum of the probabilities is equal to 1.

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