Let u1, u2, · · · , un be independent uniform random variables over [0, ? ] with the probability density function (p. d.f) f(x) = 1 ? , x ? [0, ? ], ? > 0. let u(1), u(2), · · · , u(n) be the order statistics. also let x = u(1)/u(n) and y = u(n) . (a) (5pts) find the joint probability density function of (x, y ). (b) (5pts) from part (a), show that x and y are independent variables

Plz hurry finals a paper cup in the shape of an inverted cone is 8 inches tall and has a radius of 1.5 inches. how much water can the cup hold? use 3.14 for pi. round the answer to the nearest tenth. a) 12.6 cubic in. b) 18.8 cubic in. c) 37.7 cubic in. d) 56.5 cubic in.

Which of the following questions describes the equation g + (-4) = -5? a)what number, when added to negative four, is equal to negative five? b)what number, when added to negative five, is equal to negative four? c)what number, when subtracted from negative four, is equal to negative five? d)what number, when subtracted from negative five, is equal to negative four?

To keep cylindrical tanks from tipping over, a designer is planning to enlarge the original area of the base by 50%. the new tank should have the same volume as the original. how should the designer change the height of the tank? a: make it 50% taller than the height of the original tank. b: make it 6623% taller than the height of the original tank c: make it 3313% shorter than the height of the original tank d: make it 50% shorter than the height of the original tank.