
This distribution has expectation
![E[X]=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\int_1^\infty\frac3{x^3}\,\mathrm dx=\frac32](https://tex.z-dn.net/?f=E%5BX%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20xf_X%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_1%5E%5Cinfty%5Cfrac3%7Bx%5E3%7D%5C%2C%5Cmathrm%20dx%3D%5Cfrac32)
a. The probability that
falls below the average/expectation is

b. Denote by
the largest of the three claims
. Then the density of this maximum order statistic is

where
is the distribution function for
. This is given by

So we have

and the expectation is
![E[X_{(3)}]=\displaystyle\int_{-\infty}^\infty xf_{X_{(3)}}(x)\,\mathrm dx=\int_1^\infty\frac9{x^3}\left(1-\frac1{x^3}\right)^2\,\mathrm dx=\frac{81}{40}=\boxed{2.025}](https://tex.z-dn.net/?f=E%5BX_%7B%283%29%7D%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20xf_%7BX_%7B%283%29%7D%7D%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_1%5E%5Cinfty%5Cfrac9%7Bx%5E3%7D%5Cleft%281-%5Cfrac1%7Bx%5E3%7D%5Cright%29%5E2%5C%2C%5Cmathrm%20dx%3D%5Cfrac%7B81%7D%7B40%7D%3D%5Cboxed%7B2.025%7D)
c. Denote by
the smallest of the three claims.
has density

so the expectation is
![E[X_{(1)}]=\displaystyle\int_{-\infty}^\infty xf_{X_{(1)}}(x)\,\mathrm dx=\int_1^\infty\frac9{x^9}\,\mathrm dx=\frac98=\boxed{1.125}](https://tex.z-dn.net/?f=E%5BX_%7B%281%29%7D%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20xf_%7BX_%7B%281%29%7D%7D%28x%29%5C%2C%5Cmathrm%20dx%3D%5Cint_1%5E%5Cinfty%5Cfrac9%7Bx%5E9%7D%5C%2C%5Cmathrm%20dx%3D%5Cfrac98%3D%5Cboxed%7B1.125%7D)
Answer:
C, D and E
Step-by-step explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined.
Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non zero for these values then they are vertical asymptotes.
solve 3x(x - 1)(x + 5) = 0
Equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 1 = 0 ⇒ x = 1
x + 5 = 0 ⇒ x = - 5
Vertical asymptotes at x = -5, x = 1 and x = 0
The associative property states that we can regroup the terms of an expression and obtain the same result.
We have then:

The expression that complies with this property is given by:

Answer:
An equation that shows an example of the associative property of addition is:
a. (- 4 + i) + 4i = -4 + (i + 4i)
Answer:
4.08 km
Step-by-step explanation:
we must know what is the speed of sound to determine the distance at which the ray originated
The speed at which the sound of lightning travels is approximately 0.340km/s
then
d = 0.340km/s*12 s= 4.08 km