please give me solution to the problem I am wrong ## Understanding Weibull Distribution in Disease Spread### IntroductionOnce an individual has been infected with a certain disease, let \( X \) represent the time (in days) that elapses before the individual becomes infectious. A study suggests using a Weibull distribution characterized by parameters \( \alpha = 2.1 \), \( \beta = 1.1 \), and a threshold parameter \( \gamma = 0.5 \), to model this scenario. The Weibull probability density function is given as follows:\[f(x; \alpha, \beta) = \begin{cases} \frac{\alpha}{\beta^\alpha} x^{\alpha - 1} e^{-(x/\beta)^\alpha}, & x \geq 0 \\0, & x < 0 \end{cases}\]### Calculation Tasks**(a) Calculate \( P(1 < X < 2) \):**Find the probability that \( X \) is between 1 and 2 days. Round your answer to four decimal places.**(b) Calculate \( P(X > 1.5) \):**Determine the probability that \( X \) exceeds 1.5 days. Round your answer to four decimal places.**(c) 90th Percentile Determination:**Compute the 90th percentile of the distribution, which indicates the time by which 90% of individuals will have become infectious. Round your answer to three decimal places.**(d) Mean and Standard Deviation:**Calculate the mean and standard deviation of \( X \). Round the mean to three decimal places and the standard deviation to three decimal places. The standard deviation provided is 0.487 days.This elaborative breakdown and calculations aid in comprehending the use of the Weibull distribution in estimating the timing of disease spread.

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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 = 2.1, ß = 1.1, 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, ß) = 103 far to Ba 0 -1e-(x/B) a x 20 x < 0 by x - y and x ≥ 0 by x ≥ y.] (a) Calculate P(1 < X < 2). (Round your answer to four decimal places.) X (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 standard deviation 0.487 (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean X days 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 = 2.1, ß = 1.1, 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, ß) = 103 far to Ba 0 -1e-(x/B) a x 20 x < 0 by x - y and x ≥ 0 by x ≥ y.] (a) Calculate P(1 < X < 2). (Round your answer to four decimal places.) X (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 standard deviation 0.487 (d) What are the mean and standard deviation of X? (Round your answers to three decimal places.) mean X days 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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