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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
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.)
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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