Let x be a Poisson random variable with u = 8.5. Find the probabilities for x using the Poisson formula. (Round your answers to six decimal places.) P(x = 0) P(x = 1) P(x = 2) P(x s 2)
Let x be a Poisson random variable with u = 8.5. Find the probabilities for x using the Poisson formula. (Round your answers to six decimal places.) P(x = 0) P(x = 1) P(x = 2) P(x s 2)
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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![**Poisson Probability Calculation**
Let \( x \) be a Poisson random variable with \( \mu = 8.5 \). Find the probabilities for \( x \) using the Poisson formula. (Round your answers to six decimal places.)
- \( P(x = 0) \)
- [Answer box]
- \( P(x = 1) \)
- [Answer box]
- \( P(x = 2) \)
- [Answer box]
- \( P(x \leq 2) \)
- [Answer box]
**Explanation**: The Poisson formula is given by:
\[ P(x; \mu) = \frac{e^{-\mu} \mu^x}{x!} \]
Where \( e \) is the base of the natural logarithm, \( \mu \) is the average number of occurrences in the interval, and \( x \) is the actual number of events that occur. Fill in the answers for each condition above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fdf87a1-6c5c-465d-8ddf-eaf69800c0eb%2F9e1c3af6-035d-453c-ac8b-73005e53bb47%2Fy0tijz_processed.png&w=3840&q=75)
Transcribed Image Text:**Poisson Probability Calculation**
Let \( x \) be a Poisson random variable with \( \mu = 8.5 \). Find the probabilities for \( x \) using the Poisson formula. (Round your answers to six decimal places.)
- \( P(x = 0) \)
- [Answer box]
- \( P(x = 1) \)
- [Answer box]
- \( P(x = 2) \)
- [Answer box]
- \( P(x \leq 2) \)
- [Answer box]
**Explanation**: The Poisson formula is given by:
\[ P(x; \mu) = \frac{e^{-\mu} \mu^x}{x!} \]
Where \( e \) is the base of the natural logarithm, \( \mu \) is the average number of occurrences in the interval, and \( x \) is the actual number of events that occur. Fill in the answers for each condition above.
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