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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) O 0.29 2 0.37 0.11

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) O 0.29 2 0.37 0.11

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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**Understanding Discrete Probability Distributions** In this exercise, we aim to determine the missing probability value in a discrete probability distribution. A probability distribution must satisfy two main conditions: 1. Each probability must be between 0 and 1, inclusive. 2. The sum of all probabilities must equal 1. Given the following distribution table: | x | P(x) | |---|------| | 3 | 0.29 | | 4 | ? | | 5 | 0.37 | | 6 | 0.11 | We need to find the probability of \( P(4) \). To solve for the missing probability, \( P(4) \), we can set up the equation: \[ P(3) + P(4) + P(5) + P(6) = 1 \] Substitute the known values: \[ 0.29 + P(4) + 0.37 + 0.11 = 1 \] Combine the known probabilities: \[ 0.77 + P(4) = 1 \] Solve for \( P(4) \): \[ P(4) = 1 - 0.77 = 0.23 \] **Conclusion:** The missing probability, \( P(4) \), is 0.23. This completes the probability distribution, ensuring that all conditions are met.
Transcribed Image Text:**Understanding Discrete Probability Distributions** In this exercise, we aim to determine the missing probability value in a discrete probability distribution. A probability distribution must satisfy two main conditions: 1. Each probability must be between 0 and 1, inclusive. 2. The sum of all probabilities must equal 1. Given the following distribution table: | x | P(x) | |---|------| | 3 | 0.29 | | 4 | ? | | 5 | 0.37 | | 6 | 0.11 | We need to find the probability of \( P(4) \). To solve for the missing probability, \( P(4) \), we can set up the equation: \[ P(3) + P(4) + P(5) + P(6) = 1 \] Substitute the known values: \[ 0.29 + P(4) + 0.37 + 0.11 = 1 \] Combine the known probabilities: \[ 0.77 + P(4) = 1 \] Solve for \( P(4) \): \[ P(4) = 1 - 0.77 = 0.23 \] **Conclusion:** The missing probability, \( P(4) \), is 0.23. This completes the probability distribution, ensuring that all conditions are met.
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