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)
Jerry read 12 hours or 60/5 in those 20 days but I cant tell you how much in September.
1.2 is less than 1.5
If you cancel out 1 from both numbers you're left with .2 and .5
Multiply both by 10 and get 2 and 5.
Obviously 2 is less than 5.
Answer:
first evening = 21 phone calls
second evening = 11 phone calls
third evening = 84 phone calls
Step-by-step explanation:
Total phone calls = 116
Let
Number of calls in the first evening = x
The second evening = x - 10
The third evening = 4x
Total phone calls = first evening + second evening + third evening
116 = x + (x - 10) + 4x
116 = x + x - 10 + 4x
116 + 10 = 6x
126 = 6x
x = 126 / 6
x = 21 phone calls
Number of calls in the first evening = x
= 21 phone calls
The second evening = x - 10
= 21 - 10
= 11 phone calls
The third evening = 4x
= 4(21)
= 84 phone calls
Answer:
4
Step-by-step explanation:16 / 4 =4 hope this helps please give brainliest will be first
