Answer: 5x^4
Step-by-step explanation: When simplifying combine like terms, in this case all X's will be combined together to make x^4, the 5 would be left alone.
x*5*x*x*x= 5 * x*x*x*x = 5x^4
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:
The case is in the deliberation phase, and the jury selection will follow.
Step-by-step explanation:
As you may already know, a jury is a court with the active and influential participation of citizens who have been called upon to decide whether a defendant is guilty or not of the crimes being accused. Generally, the jury is summoned for crimes that offered someone life risks.
The citizens chosen to represent the jury will be selected shortly after the decision-making phase. The selection of the jury allows defense and prosecution attorneys to question the reason why each citizen was selected.
Ratio=4.0 *10⁷ Krill / day
amount of krill=ratio * days
amount of krill=(4.0*10⁷ Krill /day)(3.65*10² days)=1.46*10¹⁰ krill
Answer: 1.46*10¹⁰ krill
