An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string = the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). For each outcome, let N be the random variable counting the number of odd rolls in each outcome. For example, if the outcome is eoe, then N (eoe) = 1. Suppose that the random variable X is defined in terms of N as follows: X = N²-N-1. The values of X are given in the table below. Outcome eoe eee ooe oee eoo oeo 000 eeo Value of X-1 -1 1 -1 1 1 5 -1 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P (X=x) Check 0 0 0 0 n olo C X $ 33 Oll Save For Later Submit Ass Ⓒ2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center 19
An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string = the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). For each outcome, let N be the random variable counting the number of odd rolls in each outcome. For example, if the outcome is eoe, then N (eoe) = 1. Suppose that the random variable X is defined in terms of N as follows: X = N²-N-1. The values of X are given in the table below. Outcome eoe eee ooe oee eoo oeo 000 eeo Value of X-1 -1 1 -1 1 1 5 -1 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P (X=x) Check 0 0 0 0 n olo C X $ 33 Oll Save For Later Submit Ass Ⓒ2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center 19
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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![**Transcription for Educational Website: Probability and Outcomes of a Fair Die**
---
An unbiased die (fair die) is rolled three times. For each roll, we are interested in determining whether the roll results in an odd or even number. Each outcome is represented by a string like "oee," where "o" denotes an odd number and "e" denotes an even number. Thus, "oee" signifies an odd number on the first roll, followed by even numbers on the second and third rolls.
For each outcome, let \( N \) be the random variable that counts the number of odd rolls in each outcome. For instance, if the outcome is "eoe," then \( N(eoe) = 1 \).
The random variable \( X \) is defined in terms of \( N \) using the formula: \( X = N^2 - N - 1 \). Below is a table displaying the values of \( X \) for various outcomes:
| Outcome | eoe | eee | oee | ooo | eoo | oeo | eeo |
|---------|-----|-----|-----|-----|-----|-----|-----|
| Value of \( X \) | -1 | -1 | -1 | 5 | 1 | 1 | -1 |
Your task is to calculate the probabilities \( P(X = x) \) of the probability distribution of \( X \). First, complete the first row by filling in the values of \( X \) and then fill in the corresponding probabilities in the second row.
The diagram below is designed for inputting this data:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Value } x \text{ of } X & \Box & \Box & \Box & \Box \\
\hline
P(X = x) & \Box & \Box & \Box & \Box \\
\hline
\end{array}
\]
[Button: Check]
[Buttons: Save For Later | Submit Assignment]
---
© 2023 McGraw Hill LLC. All Rights Reserved.
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**End of Educational Material**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5557f798-50fc-42ce-981e-d78a8f9a82ca%2F7e88bdd3-8307-43bf-b309-ce474c9bf8b1%2Fn4t3jwl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website: Probability and Outcomes of a Fair Die**
---
An unbiased die (fair die) is rolled three times. For each roll, we are interested in determining whether the roll results in an odd or even number. Each outcome is represented by a string like "oee," where "o" denotes an odd number and "e" denotes an even number. Thus, "oee" signifies an odd number on the first roll, followed by even numbers on the second and third rolls.
For each outcome, let \( N \) be the random variable that counts the number of odd rolls in each outcome. For instance, if the outcome is "eoe," then \( N(eoe) = 1 \).
The random variable \( X \) is defined in terms of \( N \) using the formula: \( X = N^2 - N - 1 \). Below is a table displaying the values of \( X \) for various outcomes:
| Outcome | eoe | eee | oee | ooo | eoo | oeo | eeo |
|---------|-----|-----|-----|-----|-----|-----|-----|
| Value of \( X \) | -1 | -1 | -1 | 5 | 1 | 1 | -1 |
Your task is to calculate the probabilities \( P(X = x) \) of the probability distribution of \( X \). First, complete the first row by filling in the values of \( X \) and then fill in the corresponding probabilities in the second row.
The diagram below is designed for inputting this data:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Value } x \text{ of } X & \Box & \Box & \Box & \Box \\
\hline
P(X = x) & \Box & \Box & \Box & \Box \\
\hline
\end{array}
\]
[Button: Check]
[Buttons: Save For Later | Submit Assignment]
---
© 2023 McGraw Hill LLC. All Rights Reserved.
Buttons for navigation:
- Chrome, Gmail, Google Calendar, Google Drive, YouTube, etc.
**End of Educational Material**
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