MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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. Buttons for navigation: - Chrome, Gmail, Google Calendar, Google Drive, YouTube, etc. **End of Educational Material**
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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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