ng lable represents a legitimate discrete probability distribution. 0.25 10 0.2 25 30 0.15 The missing value is

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**Title: Completing a Discrete Probability Distribution**

**Objective:** 
Find the missing value so that the following table represents a legitimate discrete probability distribution.

**Table:**
| \(x\) | \(P(x)\) |
|------|---------|
| 0    | 0.25    |
| 10   | 0.2     |
| 25   | ?       |
| 30   | 0.15    |

**Task:** 
Calculate the missing probability value so that the sum of all probabilities equals 1, ensuring a legitimate probability distribution.

**Solution:**
To find the missing probability \(P(25)\), add all known probabilities and subtract from 1:

\[ 0.25 + 0.2 + ? + 0.15 = 1 \]

\[ 0.6 + ? = 1 \]

\[ ? = 1 - 0.6 = 0.4 \]

**Conclusion:**
The missing value is 0.4.
Transcribed Image Text:**Title: Completing a Discrete Probability Distribution** **Objective:** Find the missing value so that the following table represents a legitimate discrete probability distribution. **Table:** | \(x\) | \(P(x)\) | |------|---------| | 0 | 0.25 | | 10 | 0.2 | | 25 | ? | | 30 | 0.15 | **Task:** Calculate the missing probability value so that the sum of all probabilities equals 1, ensuring a legitimate probability distribution. **Solution:** To find the missing probability \(P(25)\), add all known probabilities and subtract from 1: \[ 0.25 + 0.2 + ? + 0.15 = 1 \] \[ 0.6 + ? = 1 \] \[ ? = 1 - 0.6 = 0.4 \] **Conclusion:** The missing value is 0.4.
Expert Solution
Step 1

Statistics homework question answer, step 1, image 1

Determine the probability values to the probability distribution table.

 

The probability values to the probability distribution table is obtained below as follows :

 

From the information, given that

 

Statistics homework question answer, step 1, image 2

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