24. A point is selected at random from the pyramid V = (x, y, z) :...

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24. A point is selected at random from the pyramid V =



(x, y, z) : x, y, z ≥ 0, x + y + z ≤ 1


.

Letting (X, Y,Z) be its coordinates, determine if X, Y, and Z are independent.

Hint: Recall that the volume of a pyramid is Bh/3, where h is the height and B is the area of the base.

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