Answer:
Step-by-step explanation:
<u>System Determinant</u>
The determinant of the system is the determinant of the matrix of coefficients:
<u>X Determinant</u>
This is the determinant of the matrix with the x-coefficients replaced by the constants.
<u>Y Determinant</u>
This is the determinant of the matrix with the y-coefficients replaced by the constants.
_____
This problem didn't ask, but the solution is ...
x = Dx/D = -4/-2 = 2
y = Dy/D = -2/-2 = 1
(x, y) = (2, 1)
Answer:
Yes, all of your answers are 100% correct
Step-by-step explanation:
You correctly set the values equal to the numerator or denominator (minutes = minutes) and any value will equal the same value.
Answer:
172 yd²
Step-by-step explanation:
a. 
is a joint density function if its integral over the given support is 1:
so the answer is yes.
b. We should first find the density of the marginal distribution, 
:
Then
or about 0.2019.
For the other probability, we can use the joint PDF directly:
which is about 0.7326.
c. We already know the PDF for 
, so we just integrate:
![E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5](https://tex.z-dn.net/?f=E%5BY%5D%3D%5Cdisplaystyle%5Cint_%7B-%5Cinfty%7D%5E%5Cinfty%20y%5C%2Cf_Y%28y%29%5C%2C%5Cmathrm%20dy%3D%5Cfrac15%5Cint_0%5E%5Cinfty%20ye%5E%7B-y%2F5%7D%5C%2C%5Cmathrm%20dy%3D%5Cboxed5)
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