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o solve P(3 ≤ x ≤ 5) = P(x ≤ 5) - P(x ≤ 2) we need to find P(x ≤ 2) and P(x ≤ 5). We previously identified P(x ≤ 2) = 0.088. Ise Table 2 to identify P(x ≤ 5). (Round your answer to three decimal places.) "(x ≤ 5) =

o solve P(3 ≤ x ≤ 5) = P(x ≤ 5) - P(x ≤ 2) we need to find P(x ≤ 2) and P(x ≤ 5). We previously identified P(x ≤ 2) = 0.088. Ise Table 2 to identify P(x ≤ 5). (Round your answer to three decimal places.) "(x ≤ 5) =

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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**Table 2: Cumulative Poisson Probabilities** This table presents the cumulative Poisson probabilities for different values of \( \mu \) and \( k \). The tabulated values are represented by \( P(X \leq k) = p(0) + p(1) + \cdots + p(k) \), where computations are rounded to the third decimal place. ### Table Explanation: - **\( k \)**: Represents the number of events. - **\( \mu \)**: Represents the average rate of occurrence. The table lists cumulative probabilities for \( \mu \) values ranging from 0.1 to 7.0 and \( k \) values up to 17. #### Key Data Points: - **For \( \mu = 0.1 \):** - \( k = 0 \): Probability is 0.905 - \( k = 1 \): Probability is 0.995 - \( k \geq 2 \): Probability is 1.000 - **For \( \mu = 1.0 \):** - \( k = 0 \): Probability is 0.368 - \( k = 1 \): Probability is 0.736 - \( k = 2 \): Probability is 0.920 - **For \( \mu = 7.0 \):** - \( k = 0 \): Probability is 0.001 - \( k = 7 \): Probability is 0.599 - \( k = 17 \): Probability is 1.000 The probabilities increase with higher \( \mu \) and \( k \) values, demonstrating the behavior typical of Poisson distributions, where the likelihood of observing up to \( k \) events rises with an increasing average rate (\( \mu \)). This table is essential for calculating the probability of observing up to a certain number of events in a fixed interval when the average number of events is known.
Transcribed Image Text:**Table 2: Cumulative Poisson Probabilities** This table presents the cumulative Poisson probabilities for different values of \( \mu \) and \( k \). The tabulated values are represented by \( P(X \leq k) = p(0) + p(1) + \cdots + p(k) \), where computations are rounded to the third decimal place. ### Table Explanation: - **\( k \)**: Represents the number of events. - **\( \mu \)**: Represents the average rate of occurrence. The table lists cumulative probabilities for \( \mu \) values ranging from 0.1 to 7.0 and \( k \) values up to 17. #### Key Data Points: - **For \( \mu = 0.1 \):** - \( k = 0 \): Probability is 0.905 - \( k = 1 \): Probability is 0.995 - \( k \geq 2 \): Probability is 1.000 - **For \( \mu = 1.0 \):** - \( k = 0 \): Probability is 0.368 - \( k = 1 \): Probability is 0.736 - \( k = 2 \): Probability is 0.920 - **For \( \mu = 7.0 \):** - \( k = 0 \): Probability is 0.001 - \( k = 7 \): Probability is 0.599 - \( k = 17 \): Probability is 1.000 The probabilities increase with higher \( \mu \) and \( k \) values, demonstrating the behavior typical of Poisson distributions, where the likelihood of observing up to \( k \) events rises with an increasing average rate (\( \mu \)). This table is essential for calculating the probability of observing up to a certain number of events in a fixed interval when the average number of events is known.
To solve \( P(3 \leq x \leq 5) = P(x \leq 5) - P(x \leq 2) \) we need to find \( P(x \leq 2) \) and \( P(x \leq 5) \). We previously identified \( P(x \leq 2) = 0.088 \). Use Table 2 to identify \( P(x \leq 5) \). (Round your answer to three decimal places.) \( P(x \leq 5) = \underline{\hspace{1cm}} \)
Transcribed Image Text:To solve \( P(3 \leq x \leq 5) = P(x \leq 5) - P(x \leq 2) \) we need to find \( P(x \leq 2) \) and \( P(x \leq 5) \). We previously identified \( P(x \leq 2) = 0.088 \). Use Table 2 to identify \( P(x \leq 5) \). (Round your answer to three decimal places.) \( P(x \leq 5) = \underline{\hspace{1cm}} \)
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P(X≤2)=0.088 


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