Answer:

Step-by-step explanation:
Given
 --- interval
 --- 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:
 implies that:

So, we have:

Solve


Recall that:

Make x the subject

So, the cumulative density is:

 becomes
 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:
i don't know
Step-by-step explanation:
i seriously don't know