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.)\[\begin{align*}\text{mean} & \hspace{1em} \text{[ ]} \text{ days} \\\text{standard deviation} & \hspace{1em} \text{[ ]} \text{ days}\end{align*}\]

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...

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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, B = 1.8, 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, :- le-(x/B)a pa a x 2 0 f(x; а, B) %3D x 1.5). (Round your answer to four decimal places.) 0.8050 (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) 1.878 X days (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean days standard deviation days
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