Answer:
b and c are your answers
Step-by-step explanation:
Hopefully this helps :)
It is decay, growth would mean that the number in brackets is greater than 1.
Answer:
40
Step-by-step explanation:
The median is the middle value of the data arranged in ascending order. If there is no exact value in the middle then it is the average of the values either side of the middle.
The data is arranged in ascending order within the dot plot
There are 10 values in the data set
Thus the median is between the fifth and sixth values.
Counting from the left (35)
The fifth value = 39 and the sixth value = 41, thus
median =
=
= 40
By definition of covariance,
![\mathrm{Cov}(U,V)=E[(U-E[U])(V-E[V])]=E[UV-E[U]V-UE[V]+E[U]E[V]]=E[UV]-E[U]E[V]](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3DE%5B%28U-E%5BU%5D%29%28V-E%5BV%5D%29%5D%3DE%5BUV-E%5BU%5DV-UE%5BV%5D%2BE%5BU%5DE%5BV%5D%5D%3DE%5BUV%5D-E%5BU%5DE%5BV%5D)
Since
and
, we have
![E[U]=2E[X]+E[Y]-1](https://tex.z-dn.net/?f=E%5BU%5D%3D2E%5BX%5D%2BE%5BY%5D-1)
![E[V]=2E[X]-E[Y]+1](https://tex.z-dn.net/?f=E%5BV%5D%3D2E%5BX%5D-E%5BY%5D%2B1)
![\implies E[U]E[V]=(2E[X]+E[Y]-1)(2E[X]-(E[Y]-1))=4E[X]^2-(E[Y]-1)^2=4E[X]^2-E[Y]^2+2E[Y]-1](https://tex.z-dn.net/?f=%5Cimplies%20E%5BU%5DE%5BV%5D%3D%282E%5BX%5D%2BE%5BY%5D-1%29%282E%5BX%5D-%28E%5BY%5D-1%29%29%3D4E%5BX%5D%5E2-%28E%5BY%5D-1%29%5E2%3D4E%5BX%5D%5E2-E%5BY%5D%5E2%2B2E%5BY%5D-1)
and

![\implies E[UV]=4E[X^2]-E[Y^2]+2E[Y]-1](https://tex.z-dn.net/?f=%5Cimplies%20E%5BUV%5D%3D4E%5BX%5E2%5D-E%5BY%5E2%5D%2B2E%5BY%5D-1)
Putting everything together, we have
![\mathrm{Cov}(U,V)=(4E[X^2]-E[Y^2]+2E[Y]-1)-(4E[X]^2-E[Y]^2+2E[Y]-1)](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3D%284E%5BX%5E2%5D-E%5BY%5E2%5D%2B2E%5BY%5D-1%29-%284E%5BX%5D%5E2-E%5BY%5D%5E2%2B2E%5BY%5D-1%29)
![\mathrm{Cov}(U,V)=4(E[X^2]-E[X]^2)-(E[Y^2]-E[Y]^2)](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3D4%28E%5BX%5E2%5D-E%5BX%5D%5E2%29-%28E%5BY%5E2%5D-E%5BY%5D%5E2%29)
![\mathrm{Cov}(U,V)=4V[X]-V[Y]=4a-a=\boxed{3a}](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3D4V%5BX%5D-V%5BY%5D%3D4a-a%3D%5Cboxed%7B3a%7D)