Let X and Y have the joint density function 1 = x²y²' x1, y ≥ 1. Let U = 2XY and V = 2X/Y. (a) What is the joint density function of U,V? 1 f(x, y) = fu,v (u, v) = 2 vu (b) On what domain is this defined? u ≥2 and 2 ≤v≤40
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1
=
x²y²'
x1, y ≥ 1. Let U = 2XY and V = 2X/Y.
(a) What is the joint density function of U,V?
1
f(x, y) =
fu,v (u, v)
=
2
vu
(b) On what domain is this defined?
u ≥2
and
2 ≤v≤40"
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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Suppose the volume of a tree is given by V=1c²h where c is the circumference of the tree in meters at ground level and h is the height of the tree in meters. 87TT (a) Because the tree grows over time, we can assume c, h, and V are all functions of time. Find dv dt dv = dt dv dt (b) What does represent? -Select--- (c) When the tree's circumference is 4 meters and its height is 15 meters, the circumference is growing at a rate of 0.2 meters per year and the height is growing at a units --- v vI need help
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- dt t(1+(Int)³) S-Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.Find the centroid of the quarter circle x? + y <7, y 2 |x| assuming the density 6(x, y) = 1. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (*, *).) (x. y)
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