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W | P(w) 5 0.36 5.1 0.42 5.2 0.32 5.3 0.37 5.4 -0.47 No since the sum is not 1 OYes it is oNo since the variable is not discrete No since the variable must be X No for another reason not listed

W | P(w) 5 0.36 5.1 0.42 5.2 0.32 5.3 0.37 5.4 -0.47 No since the sum is not 1 OYes it is oNo since the variable is not discrete No since the variable must be X No for another reason not listed

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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Is this a probability distribution or not?

**Is this a Probability Distribution or not?** | W | P(w) | |-----|-------| | 5 | 0.36 | | 5.1 | 0.42 | | 5.2 | 0.32 | | 5.3 | 0.37 | | 5.4 | -0.47 | **Options:** - ○ No since the sum is not 1 - ○ Yes it is - ● No since the variable is not discrete - ○ No since the variable must be X - ○ No for another reason not listed **Explanation:** This table presents a dataset with two columns: \( W \) representing possible outcomes and \( P(w) \) showing the corresponding probabilities. A probability distribution must satisfy two conditions: 1. Each probability \( P(w) \) must be between 0 and 1 (inclusive). 2. The sum of all probabilities must equal 1. In this dataset, one of the probabilities is negative (\(-0.47\)), which violates the first condition. Additionally, though not required for this context, the selected answer states the issue as related to the variable not being discrete. This is not the correct rationale for invalidating the distribution based on the displayed data alone.
Transcribed Image Text:**Is this a Probability Distribution or not?** | W | P(w) | |-----|-------| | 5 | 0.36 | | 5.1 | 0.42 | | 5.2 | 0.32 | | 5.3 | 0.37 | | 5.4 | -0.47 | **Options:** - ○ No since the sum is not 1 - ○ Yes it is - ● No since the variable is not discrete - ○ No since the variable must be X - ○ No for another reason not listed **Explanation:** This table presents a dataset with two columns: \( W \) representing possible outcomes and \( P(w) \) showing the corresponding probabilities. A probability distribution must satisfy two conditions: 1. Each probability \( P(w) \) must be between 0 and 1 (inclusive). 2. The sum of all probabilities must equal 1. In this dataset, one of the probabilities is negative (\(-0.47\)), which violates the first condition. Additionally, though not required for this context, the selected answer states the issue as related to the variable not being discrete. This is not the correct rationale for invalidating the distribution based on the displayed data alone.
Expert Solution
Step 1

Result: Probability condition 

0≤P(Ei)≤1

Which means probability never be negative.

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