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
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F956b783b-4fe0-4d4e-808b-f2a93ebffce1%2F978eabf1-69e7-4f99-abcc-67380b6a1127%2F08f69bm_processed.jpeg&w=3840&q=75)

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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