Question
In: Statistics and Probability
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
Solutions
orchestra answered 1 year agoRelated Solutions
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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