Complete the following probability distribution table: P(X) -2 0.26 44 62 0.14 80 0.24 88 0.26

MATLAB: An Introduction with Applications
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ISBN:9781119256830
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**Educational Content on Probability Distribution Tables**

In this section, we are going to explore how to complete a probability distribution table. Below is an example of a probability distribution table that needs completion:

| X  | P(X) |
|----|------|
| -2 | 0.26 |
| 44 |      |
| 62 | 0.14 |
| 80 | 0.24 |
| 88 | 0.26 |

**Explanation:**

- **Column X** represents the values of the random variable.
- **Column P(X)** represents the probabilities associated with each of these values.

**Objective:**
The goal is to find the missing probability for the value \( X = 44 \). 

**Steps to Complete the Table:**

1. **Understand that the sum of probabilities must equal 1:**

   In any probability distribution, the total of the probabilities must always add up to 1.

2. **Calculate the missing probability:**

   To find the missing probability P(44), add up all given probabilities and subtract from 1:

   \[
   0.26 + 0.14 + 0.24 + 0.26 = 0.90
   \]

   \[
   1 - 0.90 = 0.10
   \]

3. **Fill in the missing probability:**

   Now that we've computed that P(44) = 0.10, the completed table should look like this:

   | X  | P(X) |
   |----|------|
   | -2 | 0.26 |
   | 44 | 0.10 |
   | 62 | 0.14 |
   | 80 | 0.24 |
   | 88 | 0.26 |

Having a complete probability distribution table is essential for analyzing the likelihood of different outcomes in a probabilistic scenario.
Transcribed Image Text:**Educational Content on Probability Distribution Tables** In this section, we are going to explore how to complete a probability distribution table. Below is an example of a probability distribution table that needs completion: | X | P(X) | |----|------| | -2 | 0.26 | | 44 | | | 62 | 0.14 | | 80 | 0.24 | | 88 | 0.26 | **Explanation:** - **Column X** represents the values of the random variable. - **Column P(X)** represents the probabilities associated with each of these values. **Objective:** The goal is to find the missing probability for the value \( X = 44 \). **Steps to Complete the Table:** 1. **Understand that the sum of probabilities must equal 1:** In any probability distribution, the total of the probabilities must always add up to 1. 2. **Calculate the missing probability:** To find the missing probability P(44), add up all given probabilities and subtract from 1: \[ 0.26 + 0.14 + 0.24 + 0.26 = 0.90 \] \[ 1 - 0.90 = 0.10 \] 3. **Fill in the missing probability:** Now that we've computed that P(44) = 0.10, the completed table should look like this: | X | P(X) | |----|------| | -2 | 0.26 | | 44 | 0.10 | | 62 | 0.14 | | 80 | 0.24 | | 88 | 0.26 | Having a complete probability distribution table is essential for analyzing the likelihood of different outcomes in a probabilistic scenario.
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