**Analyzing Probability Distributions: Number of Televisions in a Household** This educational module focuses on understanding probability distributions by analyzing the number of televisions in households within a specific country. **Task Overview:** 1. **Determine if the table represents a probability distribution.** *Answer with YES or NO.* 2. **Calculate the mean** (to one decimal place). 3. **Calculate the variance** (to two decimal places). 4. **Calculate the standard deviation** (to one decimal place). **Data Table: Number of Televisions in a Household** | x | P(x) | |---|-------| | 0 | 0.04 | | 1 | 0.12 | | 2 | 0.22 | | 3 | 0.37 | | 4 | 0.14 | | 5 | 0.11 | **Guidance on Calculations:** - **Probability Distribution Check:** Verify that the probabilities (P(x)) sum to 1 and that all probabilities are between 0 and 1. - **Mean Calculation:** Compute using the formula \(\mu = \sum [x \cdot P(x)]\). - **Variance Calculation:** Use \(\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)]\). - **Standard Deviation Calculation:** Take the square root of the variance, \(\sigma = \sqrt{\sigma^2}\). Use this activity to gain a better understanding of the characteristics and computations associated with probability distributions.
**Analyzing Probability Distributions: Number of Televisions in a Household** This educational module focuses on understanding probability distributions by analyzing the number of televisions in households within a specific country. **Task Overview:** 1. **Determine if the table represents a probability distribution.** *Answer with YES or NO.* 2. **Calculate the mean** (to one decimal place). 3. **Calculate the variance** (to two decimal places). 4. **Calculate the standard deviation** (to one decimal place). **Data Table: Number of Televisions in a Household** | x | P(x) | |---|-------| | 0 | 0.04 | | 1 | 0.12 | | 2 | 0.22 | | 3 | 0.37 | | 4 | 0.14 | | 5 | 0.11 | **Guidance on Calculations:** - **Probability Distribution Check:** Verify that the probabilities (P(x)) sum to 1 and that all probabilities are between 0 and 1. - **Mean Calculation:** Compute using the formula \(\mu = \sum [x \cdot P(x)]\). - **Variance Calculation:** Use \(\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)]\). - **Standard Deviation Calculation:** Take the square root of the variance, \(\sigma = \sqrt{\sigma^2}\). Use this activity to gain a better understanding of the characteristics and computations associated with probability distributions.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Analyzing Probability Distributions: Number of Televisions in a Household**
This educational module focuses on understanding probability distributions by analyzing the number of televisions in households within a specific country.
**Task Overview:**
1. **Determine if the table represents a probability distribution.**
*Answer with YES or NO.*
2. **Calculate the mean** (to one decimal place).
3. **Calculate the variance** (to two decimal places).
4. **Calculate the standard deviation** (to one decimal place).
**Data Table: Number of Televisions in a Household**
| x | P(x) |
|---|-------|
| 0 | 0.04 |
| 1 | 0.12 |
| 2 | 0.22 |
| 3 | 0.37 |
| 4 | 0.14 |
| 5 | 0.11 |
**Guidance on Calculations:**
- **Probability Distribution Check:** Verify that the probabilities (P(x)) sum to 1 and that all probabilities are between 0 and 1.
- **Mean Calculation:** Compute using the formula \(\mu = \sum [x \cdot P(x)]\).
- **Variance Calculation:** Use \(\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)]\).
- **Standard Deviation Calculation:** Take the square root of the variance, \(\sigma = \sqrt{\sigma^2}\).
Use this activity to gain a better understanding of the characteristics and computations associated with probability distributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9342963b-00c0-41d9-83de-b2db996dfa23%2Fe3f8af95-c869-4925-be86-037deda03c8b%2Fxlr8od.jpeg&w=3840&q=75)
Transcribed Image Text:**Analyzing Probability Distributions: Number of Televisions in a Household**
This educational module focuses on understanding probability distributions by analyzing the number of televisions in households within a specific country.
**Task Overview:**
1. **Determine if the table represents a probability distribution.**
*Answer with YES or NO.*
2. **Calculate the mean** (to one decimal place).
3. **Calculate the variance** (to two decimal places).
4. **Calculate the standard deviation** (to one decimal place).
**Data Table: Number of Televisions in a Household**
| x | P(x) |
|---|-------|
| 0 | 0.04 |
| 1 | 0.12 |
| 2 | 0.22 |
| 3 | 0.37 |
| 4 | 0.14 |
| 5 | 0.11 |
**Guidance on Calculations:**
- **Probability Distribution Check:** Verify that the probabilities (P(x)) sum to 1 and that all probabilities are between 0 and 1.
- **Mean Calculation:** Compute using the formula \(\mu = \sum [x \cdot P(x)]\).
- **Variance Calculation:** Use \(\sigma^2 = \sum [(x - \mu)^2 \cdot P(x)]\).
- **Standard Deviation Calculation:** Take the square root of the variance, \(\sigma = \sqrt{\sigma^2}\).
Use this activity to gain a better understanding of the characteristics and computations associated with probability distributions.
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