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:
h(0)= -7
Step-by-step explanation:
that is my answer
Answer:
-90 - (-144)
Step-by-step explanation:
Here you go!
Since we're depositing, you'll add the three numbers.
45 + 27 + 18 = $90
Cody deposits 90 dollars in total.
If you write checks, the numbers go down. So you'll add them, and then subtract that by the 90 dollars Cody deposits.
You'll end up with:
45 + 27 + 18 - (21 + 93)
This can simplify to..
90 - (21 + 93)
But wait! Let's add what's in the parenthesis!
93 + 21 = 144
90 - 144 = t
t = -54
Solving this equation will give you: -54
But the simple way is -90 - (-144)
Answer:
height is 4 in
Step-by-step explanation:
total area 72
divide area by base length
72/18= 4
72 total area
18 base length
4 height
155.84 gallons
150.4 minutes
surface area is multiplied by 4; surface area is multiplied by 9
922.5 cm³ ; 410 cm²
4 centimeters
2,400 apples
π/2 = 1.5708... ft²
