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:

what is the answer?

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!