Suppose that the length of a side of a cube X is uniformly distributed in the interval 9

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

Expand

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

Differentiate F(x) to give:

So:

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17

c

step-by-step explanation: