Answer only please. **Educational Content: Validity of Subjective Probability Assignments**---### A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment:- $ P(E_1) = 0.05 $- $ P(E_2) = 0.15 $- $ P(E_3) = 0.40 $- $ P(E_4) = 0.35 $#### Question: Are these probability assignments valid? Explain your reasoning.### Options:1. **No, the probabilities do not sum to 1.**2. **Yes, $ 0 \leq P(E_i) \leq 1 $ for all $ i $ and the probabilities' sum is greater than 1.**3. **Yes, $ 0 \leq P(E_i) \leq 1 $ for all $ i $ and the probabilities' sum is less than 1.**4. **No, the subjective method requires that all probabilities be equal.**### Explanation:To determine the validity of the probability assignments, we need to ensure the following conditions are met:1. Each probability $ P(E_i) $ must be between 0 and 1 (inclusive).2. The sum of all probabilities must equal 1.**Calculations:**First, let's check sum of the probabilities assigned:\[ P(E_1) + P(E_2) + P(E_3) + P(E_4) = 0.05 + 0.15 + 0.40 + 0.35 = 0.95 \]The sum of the probabilities is $ 0.95 $, which is less than 1.Therefore, the correct answer is:**Option 3: Yes, $ 0 \leq P(E_i) \leq 1 $ for all $ i $ and the probabilities' sum is less than 1.**### Additional Resources:Need more help understanding probability assignments? Check out our detailed guide on **[Understanding Probabilities and Their Properties](#)**.---Feel free to **show your work** below by explaining the steps or reasoning you used to reach this conclusion. This can add bonus points towards your score.**Note:**You can submit your work an unlimited number of times.### Upload Your WorkHave a detailed explanation or a file with your calculations? Upload

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Description: Answer only please. **Educational Content: Validity of Subjective Probability Assignments**---### A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment:- $ P(E_1) = 0.05 $- $ P(E_2) = 0.15 $- \(

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12.5 Points] DETAILS ASWESBE9 4.E.007. MY NOTES ASK YOUR TEACHER PRACTICE A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E,) = 0.05, P(E,) = 0.15, P(E,) = 0.40, and P(E) = 0.35. Are these probability assignments valid? Explain. No, the probabilities do not sum to 1. Yes, 0 s P(E) <1 for all i and the probabilities' sum is greater than 1. Yes, 0 S P(E)s1 for all i and the probabilities' sum is less than 1. O No, the subjective method requires that all probabilities be equal. Need Help? Read It O Show My Work (Optional) ? What steps or reasoning did you use? Your work may add bonus points towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display O Upload File

12.5 Points] DETAILS ASWESBE9 4.E.007. MY NOTES ASK YOUR TEACHER PRACTICE A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E,) = 0.05, P(E,) = 0.15, P(E,) = 0.40, and P(E) = 0.35. Are these probability assignments valid? Explain. No, the probabilities do not sum to 1. Yes, 0 s P(E) <1 for all i and the probabilities' sum is greater than 1. Yes, 0 S P(E)s1 for all i and the probabilities' sum is less than 1. O No, the subjective method requires that all probabilities be equal. Need Help? Read It O Show My Work (Optional) ? What steps or reasoning did you use? Your work may add bonus points towards your score. You can submit show my work an unlimited number of times. Uploaded File (10 file maximum) No Files to Display O Upload File

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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Question

Answer only please.

**Educational Content: Validity of Subjective Probability Assignments**

---

### A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment:

- $ P(E_1) = 0.05 $
- $ P(E_2) = 0.15 $
- $ P(E_3) = 0.40 $
- $ P(E_4) = 0.35 $

#### Question:
Are these probability assignments valid? Explain your reasoning.

### Options:

1. **No, the probabilities do not sum to 1.**
2. **Yes, $ 0 \leq P(E_i) \leq 1 $ for all $ i $ and the probabilities' sum is greater than 1.**
3. **Yes, $ 0 \leq P(E_i) \leq 1 $ for all $ i $ and the probabilities' sum is less than 1.**
4. **No, the subjective method requires that all probabilities be equal.**

### Explanation:

To determine the validity of the probability assignments, we need to ensure the following conditions are met:
1. Each probability $ P(E_i) $ must be between 0 and 1 (inclusive).
2. The sum of all probabilities must equal 1.

**Calculations:**

First, let's check sum of the probabilities assigned:

\[ P(E_1) + P(E_2) + P(E_3) + P(E_4) = 0.05 + 0.15 + 0.40 + 0.35 = 0.95 \]

The sum of the probabilities is $ 0.95 $, which is less than 1.

Therefore, the correct answer is:

**Option 3: Yes, $ 0 \leq P(E_i) \leq 1 $ for all $ i $ and the probabilities' sum is less than 1.**

### Additional Resources:
Need more help understanding probability assignments? Check out our detailed guide on **[Understanding Probabilities and Their Properties](#)**.

---

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