Answer: 10.63
Step-by-step explanation: 8.1 + 2.53
Answer:

Step-by-step explanation:
Given
--- interval
Required
The probability density of the volume of the cube
The volume of a cube is:

For a uniform distribution, we have:

and

implies that:

So, we have:

Solve


Recall that:

Make x the subject

So, the cumulative density is:

becomes

The CDF is:

Integrate
![F(x) = [v]\limits^{v^\frac{1}{3}}_9](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Bv%5D%5Climits%5E%7Bv%5E%5Cfrac%7B1%7D%7B3%7D%7D_9)
Expand

The density function of the volume F(v) is:

Differentiate F(x) to give:




So:

Answer: a) Yes
b) No
Explanation: Substitute the values of X and Y from the given points into the equation. I’ll use a) as an example:
Given point: (1,-3)
Equation: 4x-2y=10
Value of X: 1
Value of Y: -3
Substitute X and Y: 4(1)-2(-3)=10
4-(-6)=10
4+6=10 ✔︎
Therefore, the given ordered pair is a proper solution to the equation 4x-2y=10.
*You can use the same method for question b).*