It still says the mean is wrong in part D. 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,\[f(x; \alpha, \beta) = \begin{cases} \frac{\alpha}{\beta^{\alpha}} (x - \gamma)^{\alpha - 1} e^{-(x/\beta)^\alpha} & x \geq \gamma \\0 & x < 0 \end{cases}\]by $ x - \gamma $ and $ x \geq 0 $ by $ x \geq \gamma $.**(a)** Calculate $ P(1 < X < 2) $. (Round your answer to four decimal places.)\[0.4737 \quad \checkmark\]**(b)** Calculate $ P(X > 1.5) $. (Round your answer to four decimal places.)\[0.7775 \quad \checkmark\]**(c)** What is the 90th percentile of the distribution? (Round your answer to three decimal places.)\[2.843 \quad \text{days} \quad \checkmark\]**(d)** What are the mean and standard deviation of $ X $? (Round your answers to three decimal places.)\[\begin{align*}\text{mean} & \quad 1.510 \quad \text{x} \\\text{standard deviation} & \quad 0.624 \quad \text{days} \quad \checkmark\end{align*}\]

Answered: Once an individual has been infected…

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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Related questions

Question

It still says the mean is wrong in part D.

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,

\[
f(x; \alpha, \beta) =
\begin{cases}
\frac{\alpha}{\beta^{\alpha}} (x - \gamma)^{\alpha - 1} e^{-(x/\beta)^\alpha} & x \geq \gamma \\
0 & x < 0
\end{cases}
\]

by $ x - \gamma $ and $ x \geq 0 $ by $ x \geq \gamma $.

**(a)** Calculate $ P(1 < X < 2) $. (Round your answer to four decimal places.)

\[
0.4737 \quad \checkmark
\]

**(b)** Calculate $ P(X > 1.5) $. (Round your answer to four decimal places.)

\[
0.7775 \quad \checkmark
\]

**(c)** What is the 90th percentile of the distribution? (Round your answer to three decimal places.)

\[
2.843 \quad \text{days} \quad \checkmark
\]

**(d)** What are the mean and standard deviation of $ X $? (Round your answers to three decimal places.)

\[
\begin{align*}
\text{mean} & \quad 1.510 \quad \text{x} \\
\text{standard deviation} & \quad 0.624 \quad \text{days} \quad \checkmark
\end{align*}
\]

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1: Given information

Let f be a pdf

$f left parenthesis x comma alpha comma beta right parenthesis space equals space alpha over beta to the power of alpha x to the power of alpha minus 1 end exponent e to the power of negative left parenthesis x divided by beta right parenthesis to the power of alpha end exponent$ ; x>=0

= 0 ; x<0

$alpha equals space 2.6 beta equals 1.7 gamma equals 0.5$