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:

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

she will most likely have 33  

step-by-step explanation: