Once an individual has been infected with a certain disease, let X represent the time (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 α = 2.6, β = 1.1, and γ = 0.5. [Hint: The two-parameter Weibull distribution can be generalized by introducing a third parameter γ, called a threshold or location parameter: replace x in the equation below, f(x; α, β) = α βα xα − 1e−(x/β)α x ≥ 0 0 x < 0 by x − γ and x ≥ 0 by x ≥ γ.] (a) Calculate P(1 < X < 2). (Round your answer to four decimal places.) (b) Calculate P(X > 1.5). (Round your answer to four decimal places.) (c) What is the 90th percentile of the distribution? (Round your answer to three decimal places.) 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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orchestra answered 1 year ago

Once an individual has been infected with a certain disease, let X represent the time (days)...

Once an individual has been infected with a certain disease, let X represent the time (days) that elapses before the individual becomes infectious. The article “The Probability of Containment for Multitype Branching Process Models for Emerging Epidemics” (J. of Applied Probability, 2011: 173-188) proposes a Weibull distribution with alpha = 2.2, beta = 1.1, and gamma = 0.5 a. Calculate P(1 < X < 2). b. Calculate P(X > 1.5). c. What is the 90th percentile of the distribution? d....

Here is another infectious disease model. Once a person becomes infected, the time X, in days,...

Here is another infectious disease model. Once a person becomes infected, the time X, in days, until the person becomes infectious (can pass on the disease) can be modeled as a Weibull random variable with density function f(x,α,β) = (α/βα)xα−1e−(x/β)α for 0 ≤ x ≤ ∞ and 0 otherwise with α = 3.7 and β = 7.1 α is the shape parameter and β is the scale parameter. Hint: Solve this with the built-in R functions for the Weibull...

Here is another infectious disease model. Once a person becomes infected, the time X, in days,...

Here is another infectious disease model. Once a person becomes infected, the time X, in days, until the person becomes infectious (can pass on the disease) can be modeled as a Weibull random variable with density function f(x,α,β) = (α/βα)xα−1e−(x/β)α for 0 ≤ x ≤ ∞ and 0 otherwise with α = 3.7 and β = 7.1 α is the shape parameter and β is the scale parameter. Hint: Solve this with the built-in R functions for the Weibull...

Here is another infectious disease model. Once a person becomes infected, the time X, in days,...

Here is another infectious disease model. Once a person becomes infected, the time X, in days, until the person becomes infectious (can pass on the disease) can be modeled as a Weibull random variable with density function f(x,α,β) = α βα xα−1e−(x/β)α for 0 ≤ x ≤ ∞ and 0 otherwise with α = 3.7 and β = 7.1 α is the shape parameter and β is the scale parameter. Hint: Solve this with the built-in R functions for the...

Let X represent the full height of a certain species of tree. Assume that X has...

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 77 ft and a standard deviation of 3.5 ft. A tree of this type grows in my backyard, and it stands 65.8 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. P(X<65.8)= My neighbor also has a tree of this type growing in her backyard,...

Annual high temperatures in a certain location have been tracked for several years. Let X represent...

Annual high temperatures in a certain location have been tracked for several years. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places). x y 2 34.82 3 33.28 4 34.84 5 35.1 6 33.26 7 35.42 8 34.18 9 34.54 10 34.4 11 35.86 12 35.12 13 37.88 The equation is? Interpret the slope For each...

Annual high temperatures in a certain location have been tracked for several years. Let X represent...

Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. At the 0.01 significance level, does the data below show significant (linear) correlation between X and Y? x y 5 36.63 6 35.9 7 35.77 8 38.64 9 30.51 10 29.68 11 30.35 12 21.42 13 19.99 14 18.26 15 12.03 16 15.8 Yes, significant correlation No

Annual high temperatures in a certain location have been tracked for several years. Let X represent...

Annual high temperatures in a certain location have been tracked for several years. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places). x y 3 35.01 4 35.38 5 37.75 6 36.12 7 36.49 8 40.16 9 38.93 10 39.7 11 42.77 12 43.24 13 42.11 14 44.08 The equation is ˆ y = x +...

it has been hypothesized that the average germination time for a certain seed is 4 days....

it has been hypothesized that the average germination time for a certain seed is 4 days. an experiment involving 32 seeds revealed an average germination time of 6 days. at the level of significance 0.05. is there evidence that average germination times has increased? (standard deviation=0.80 days). P-value method

1)Annual high temperatures in a certain location have been tracked for several years. Let X represent...

1)Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = _____________ x + ________________ x y 3 10.42 4 10.96 5 13.8 6 17.14 7 16.98 8 21.22 9 23.96 10 23.9 11 27.14 12 30.28 13 30.22 14 34.06 15 37.1 16 36.74 17 41.08 18 41.62 2)...

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Once an individual has been infected with a certain disease, let X represent the time (days)...

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Once an individual has been infected with a certain disease, let X represent the time (days)...

Here is another infectious disease model. Once a person becomes infected, the time X, in days,...

Here is another infectious disease model. Once a person becomes infected, the time X, in days,...

Here is another infectious disease model. Once a person becomes infected, the time X, in days,...

Let X represent the full height of a certain species of tree. Assume that X has...

Annual high temperatures in a certain location have been tracked for several years. Let X represent...

Annual high temperatures in a certain location have been tracked for several years. Let X represent...

Annual high temperatures in a certain location have been tracked for several years. Let X represent...

it has been hypothesized that the average germination time for a certain seed is 4 days....

1)Annual high temperatures in a certain location have been tracked for several years. Let X represent...