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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.

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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