Homework Help is Here – Start Your Trial Now!
Math
Statistics
Let x be a Poisson random variable with μ = 4.5. Find the probabilities for x using Table 2. (Round your answers to three decimal places.) P(x ≤ 3) 0.342 P(x > 3) P(x = 3) X P(3 ≤ x ≤ 5)

Let x be a Poisson random variable with μ = 4.5. Find the probabilities for x using Table 2. (Round your answers to three decimal places.) P(x ≤ 3) 0.342 P(x > 3) P(x = 3) X P(3 ≤ 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
See similar textbooks
icon
Related questions
Question
**Problem Statement:** Let \( x \) be a Poisson random variable with \( \mu = 4.5 \). Find the probabilities for \( x \) using Table 2. (Round your answers to three decimal places.) **Probability Calculations:** 1. **\( P(x \leq 3) \)** Entered Value: **0.342** ✅ 2. **\( P(x > 3) \)** Value not provided. 3. **\( P(x = 3) \)** Entered Value: Incorrect ❌ 4. **\( P(3 \leq x \leq 5) \)** Value not provided. **Instructions:** Ensure all probabilities are calculated using the relevant Poisson distribution table and round your answers to three decimal places.
Transcribed Image Text:**Problem Statement:** Let \( x \) be a Poisson random variable with \( \mu = 4.5 \). Find the probabilities for \( x \) using Table 2. (Round your answers to three decimal places.) **Probability Calculations:** 1. **\( P(x \leq 3) \)** Entered Value: **0.342** ✅ 2. **\( P(x > 3) \)** Value not provided. 3. **\( P(x = 3) \)** Entered Value: Incorrect ❌ 4. **\( P(3 \leq x \leq 5) \)** Value not provided. **Instructions:** Ensure all probabilities are calculated using the relevant Poisson distribution table and round your answers to three decimal places.
### Table 2: Cumulative Poisson Probabilities This table provides cumulative Poisson probabilities, presenting values as \( P(X \leq k) = p(0) + p(1) + \cdots + p(k) \). The computations are rounded to the third decimal place. The table is structured with various values of \( \mu \), representing the mean number of events in a fixed interval, across the top and values of \( k \), representing the number of events, along the side. #### Table Breakdown: 1. **Columns and Rows:** - The top row signifies \( \mu \) values ranging from 0.1 to 7.0. - The left column indicates the \( k \) values from 0 to 17. 2. **Values in the Table:** - Each cell contains the probability that the number of events \( X \) is less than or equal to \( k \) given a particular \( \mu \). 3. **First Portion of the Table (Top):** - Deals with smaller \( \mu \) values: 0.1 to 1.5 and \( k \) values from 0 to 7. - Illustrates probabilities decreasing as \( \mu \) lowers and/or \( k \) increases. 4. **Second Portion of the Table (Bottom):** - Covers larger \( \mu \) values: 2.0 to 7.0 and \( k \) values from 0 to 17. - Shows probabilities decreasing gradually as \( k \) increases, especially pronounced in higher \( \mu \) values. 5. **Observation:** - Cumulative probabilities approach 1.000 as \( k \) increases, indicating the likelihood of observing up to \( k \) events becomes more certain with increased \( k \) or \( \mu \). This table is useful for statistical calculations involving Poisson processes, ideal for understanding the probability distribution of events happening independently within a fixed interval.
Transcribed Image Text:### Table 2: Cumulative Poisson Probabilities This table provides cumulative Poisson probabilities, presenting values as \( P(X \leq k) = p(0) + p(1) + \cdots + p(k) \). The computations are rounded to the third decimal place. The table is structured with various values of \( \mu \), representing the mean number of events in a fixed interval, across the top and values of \( k \), representing the number of events, along the side. #### Table Breakdown: 1. **Columns and Rows:** - The top row signifies \( \mu \) values ranging from 0.1 to 7.0. - The left column indicates the \( k \) values from 0 to 17. 2. **Values in the Table:** - Each cell contains the probability that the number of events \( X \) is less than or equal to \( k \) given a particular \( \mu \). 3. **First Portion of the Table (Top):** - Deals with smaller \( \mu \) values: 0.1 to 1.5 and \( k \) values from 0 to 7. - Illustrates probabilities decreasing as \( \mu \) lowers and/or \( k \) increases. 4. **Second Portion of the Table (Bottom):** - Covers larger \( \mu \) values: 2.0 to 7.0 and \( k \) values from 0 to 17. - Shows probabilities decreasing gradually as \( k \) increases, especially pronounced in higher \( \mu \) values. 5. **Observation:** - Cumulative probabilities approach 1.000 as \( k \) increases, indicating the likelihood of observing up to \( k \) events becomes more certain with increased \( k \) or \( \mu \). This table is useful for statistical calculations involving Poisson processes, ideal for understanding the probability distribution of events happening independently within a fixed interval.
Expert Solution
Step 1: Given information

X ~ Pois(μ=4.5)


steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS