Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, ß = 1.7, and y=0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below, f(x; a, B)= Ba" E -²-1-(x/B) a 0 x 20 x < 0 by xy and x 20 by x ≥ y.] (a) Calculate P(1 < X < 2). (Round your answer to four decimal places.) x standard deviation (b) Calculate P(X> 1.5). (Round your answer to four decimal places.) X (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) X days (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean X days X days
Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, ß = 1.7, and y=0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below, f(x; a, B)= Ba" E -²-1-(x/B) a 0 x 20 x < 0 by xy and x 20 by x ≥ y.] (a) Calculate P(1 < X < 2). (Round your answer to four decimal places.) x standard deviation (b) Calculate P(X> 1.5). (Round your answer to four decimal places.) X (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) X days (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean X days X days
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
![Once an individual has been infected with a certain disease, let \( X \) represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with \( \alpha = 2.6 \), \( \beta = 1.7 \), and \( \gamma = 0.5 \).
**Hint:** The two-parameter Weibull distribution can be generalized by introducing a third parameter \( \gamma \), called a threshold or location parameter: replace \( x \) in the equation below,
\[
f(x; \alpha, \beta) =
\begin{cases}
\frac{\alpha}{\beta^\alpha} (x^{-\gamma})^{\alpha-1} e^{-(x^\gamma/\beta)^\alpha} & x \geq 0 \\
0 & x < 0
\end{cases}
\]
by \( x - \gamma \) and \( x \ge \gamma \) by \( x \ge \gamma \).
---
**(a)** Calculate \( P(1 < X < 2) \). (Round your answer to four decimal places.)
\[ \text{[ ]} \hspace{1em} \times \]
---
**(b)** Calculate \( P(X > 1.5) \). (Round your answer to four decimal places.)
\[ \text{[ ]} \hspace{1em} \times \]
---
**(c)** What is the 90th percentile of the distribution? (Round your answer to three decimal places.)
\[ \text{[ ]} \text{ days} \]
---
**(d)** What are the mean and standard deviation of \( X \)? (Round your answers to three decimal places.)
\[
\begin{align*}
\text{mean} & \hspace{1em} \text{[ ]} \text{ days} \\
\text{standard deviation} & \hspace{1em} \text{[ ]} \text{ days}
\end{align*}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76fb667-0622-451e-86fc-d3866765f8e5%2F9144fd17-1430-48e1-b467-7b6cc4460677%2Fqen68h_processed.png&w=3840&q=75)
Transcribed Image Text:Once an individual has been infected with a certain disease, let \( X \) represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with \( \alpha = 2.6 \), \( \beta = 1.7 \), and \( \gamma = 0.5 \).
**Hint:** The two-parameter Weibull distribution can be generalized by introducing a third parameter \( \gamma \), called a threshold or location parameter: replace \( x \) in the equation below,
\[
f(x; \alpha, \beta) =
\begin{cases}
\frac{\alpha}{\beta^\alpha} (x^{-\gamma})^{\alpha-1} e^{-(x^\gamma/\beta)^\alpha} & x \geq 0 \\
0 & x < 0
\end{cases}
\]
by \( x - \gamma \) and \( x \ge \gamma \) by \( x \ge \gamma \).
---
**(a)** Calculate \( P(1 < X < 2) \). (Round your answer to four decimal places.)
\[ \text{[ ]} \hspace{1em} \times \]
---
**(b)** Calculate \( P(X > 1.5) \). (Round your answer to four decimal places.)
\[ \text{[ ]} \hspace{1em} \times \]
---
**(c)** What is the 90th percentile of the distribution? (Round your answer to three decimal places.)
\[ \text{[ ]} \text{ days} \]
---
**(d)** What are the mean and standard deviation of \( X \)? (Round your answers to three decimal places.)
\[
\begin{align*}
\text{mean} & \hspace{1em} \text{[ ]} \text{ days} \\
\text{standard deviation} & \hspace{1em} \text{[ ]} \text{ days}
\end{align*}
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 9 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Can you please answer part D also?
![Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, ß = 1.7, and
y = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below,
{2.
f(x; α, B) = Ba
-1e-(x/B) a
0
by x - y and x ≥ 0 by x ≥ y.]
(a) Calculate P(1 < X < 2). (Round your answer to four decimal places.)
0.4737
mean
x ≥ 0
x < 0
(b) Calculate P(X> 1.5). (Round your answer to four decimal places.)
0.7775
✓
(c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.)
2.843
days
(d) What are the mean and standard deviation of X? (Round your answers to three decimal places.)
X days
X days
2.008
standard deviation 0.645](https://content.bartleby.com/qna-images/question/f76fb667-0622-451e-86fc-d3866765f8e5/fcb6644d-cc57-4a7d-96b6-58d0e552b822/rnoa6j1_processed.png)
Transcribed Image Text:Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. An article proposes a Weibull distribution with a = 2.6, ß = 1.7, and
y = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter y, called a threshold or location parameter: replace x in the equation below,
{2.
f(x; α, B) = Ba
-1e-(x/B) a
0
by x - y and x ≥ 0 by x ≥ y.]
(a) Calculate P(1 < X < 2). (Round your answer to four decimal places.)
0.4737
mean
x ≥ 0
x < 0
(b) Calculate P(X> 1.5). (Round your answer to four decimal places.)
0.7775
✓
(c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.)
2.843
days
(d) What are the mean and standard deviation of X? (Round your answers to three decimal places.)
X days
X days
2.008
standard deviation 0.645
Solution
by Bartleby ExpertRecommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON