Determine the required value of the missing probability to make the distribution a discrete probability distribution. P(4) = (Type an integer or a decimal.) X 3 4 5 6 P(x) 0.27 ? 0.32 0.14
Determine the required value of the missing probability to make the distribution a discrete probability distribution. P(4) = (Type an integer or a decimal.) X 3 4 5 6 P(x) 0.27 ? 0.32 0.14
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Problem: Missing Probability in a Discrete Probability Distribution
Determine the required value of the missing probability to make the distribution a discrete probability distribution.
#### Table of Probabilities:
| \( x \) | \( P(x) \) |
|---------|------------|
| 3 | 0.27 |
| 4 | ? |
| 5 | 0.32 |
| 6 | 0.14 |
#### Solution:
To make the distribution complete, the sum of all probabilities \( P(x) \) must equal 1. Therefore, we can use the following equation:
\[ P(3) + P(4) + P(5) + P(6) = 1 \]
Substituting the known values:
\[ 0.27 + P(4) + 0.32 + 0.14 = 1 \]
Solving for \( P(4) \):
\[ P(4) = 1 - (0.27 + 0.32 + 0.14) \]
\[ P(4) = 1 - 0.73 \]
\[ P(4) = 0.27 \]
Thus, the missing probability \( P(4) \) is 0.27.
**Answer:**
P(4) = \(\boxed{0.27}\) (Type an integer or a decimal.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac3be618-b645-4bd8-855b-808ff3fc18d4%2Fcf8822a4-afc2-45b8-a6d7-3c499f304da7%2Fkz8hten_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem: Missing Probability in a Discrete Probability Distribution
Determine the required value of the missing probability to make the distribution a discrete probability distribution.
#### Table of Probabilities:
| \( x \) | \( P(x) \) |
|---------|------------|
| 3 | 0.27 |
| 4 | ? |
| 5 | 0.32 |
| 6 | 0.14 |
#### Solution:
To make the distribution complete, the sum of all probabilities \( P(x) \) must equal 1. Therefore, we can use the following equation:
\[ P(3) + P(4) + P(5) + P(6) = 1 \]
Substituting the known values:
\[ 0.27 + P(4) + 0.32 + 0.14 = 1 \]
Solving for \( P(4) \):
\[ P(4) = 1 - (0.27 + 0.32 + 0.14) \]
\[ P(4) = 1 - 0.73 \]
\[ P(4) = 0.27 \]
Thus, the missing probability \( P(4) \) is 0.27.
**Answer:**
P(4) = \(\boxed{0.27}\) (Type an integer or a decimal.)
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