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2) Consider each distribution. Determine if it is a valid probability distribution or not and explain your answer. b. 1 P(x) 0.25 0.60 0.15 P(x) 0.25 0.60 0.20

2) Consider each distribution. Determine if it is a valid probability distribution or not and explain your answer. b. 1 P(x) 0.25 0.60 0.15 P(x) 0.25 0.60 0.20

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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**Analyzing Probability Distribution Validity** **Question:** Consider each distribution. Determine if it is a valid probability distribution or not and explain your answer. **Distribution a:** \[ \begin{array}{|c|c|c|c|} \hline x & 0 & 1 & 2 \\ \hline P(x) & 0.25 & 0.60 & 0.15 \\ \hline \end{array} \] **Distribution b:** \[ \begin{array}{|c|c|c|c|} \hline x & 0 & 1 & 2 \\ \hline P(x) & 0.25 & 0.60 & 0.20 \\ \hline \end{array} \] **Explanation:** For a probability distribution to be valid, the sum of all probabilities \( P(x) \) must equal 1. - **Distribution a:** \[ P(x=0) + P(x=1) + P(x=2) = 0.25 + 0.60 + 0.15 = 1.00 \] The sum equals 1, so this is a valid probability distribution. - **Distribution b:** \[ P(x=0) + P(x=1) + P(x=2) = 0.25 + 0.60 + 0.20 = 1.05 \] The sum exceeds 1, so this is not a valid probability distribution. Both distributions are evaluated on whether their probability values correctly sum up to 1. Only Distribution a meets this requirement.
Transcribed Image Text:**Analyzing Probability Distribution Validity** **Question:** Consider each distribution. Determine if it is a valid probability distribution or not and explain your answer. **Distribution a:** \[ \begin{array}{|c|c|c|c|} \hline x & 0 & 1 & 2 \\ \hline P(x) & 0.25 & 0.60 & 0.15 \\ \hline \end{array} \] **Distribution b:** \[ \begin{array}{|c|c|c|c|} \hline x & 0 & 1 & 2 \\ \hline P(x) & 0.25 & 0.60 & 0.20 \\ \hline \end{array} \] **Explanation:** For a probability distribution to be valid, the sum of all probabilities \( P(x) \) must equal 1. - **Distribution a:** \[ P(x=0) + P(x=1) + P(x=2) = 0.25 + 0.60 + 0.15 = 1.00 \] The sum equals 1, so this is a valid probability distribution. - **Distribution b:** \[ P(x=0) + P(x=1) + P(x=2) = 0.25 + 0.60 + 0.20 = 1.05 \] The sum exceeds 1, so this is not a valid probability distribution. Both distributions are evaluated on whether their probability values correctly sum up to 1. Only Distribution a meets this requirement.
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