Problem 37. Let X and Y have the joint density function f(x, y) = x>1.y>1. Let U = 3XY and V = 4X/Y. (a) What is the joint density function of U.V? Sv.x(u, v) = (b) On what domain is this defined? ">__ and 1
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- Suppose X and Y have a joint density function of f(x,y)=6x2y, 0<x<1, 0<y<1. Find P(X+2Y<1).Problem 4 The volume of the solid obtained by rotating the region enclosed by y=1/(x^3), y=0, x=2, x=7 about the y-axis can be computed using the method of cylindrical shells via an integral V=∫___________ dx (with lower limit a and upper limit b) with limits of integration a=_________ and b=__________ the volume is V= _______________ cubic unitsProblem 10 The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=2x, about the line y=0 can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower=a]____________dx with limits of integration a=________ and b=________
- Problem 7 The volume of the solid obtained by rotating the region enclosed by y=1/(x^5), y=0, x=1, x=5 about the line x=-3 can be computed using the method of cylindrical shells via an integral V=∫__________________ dx (with lower limit of a and upper limit of b) with limits of integration a=_____________ and b=______________ The volume is V=_________________cubic unitsProblem 8 The volume of the solid obtained by rotating the region enclosed by y=(e^3x)+3, y=0, x=0, x=0.2 about the x-axis can be computed using the method of disksor washers via an integral V=∫[upper limit=b, lower limit=a]______ dx with limits of integration a=______ and b=_______Suppose f(x)=3x2, 0<x<1 is a density function of X. Find P(1/2<X<2).
- Problem 11 The volume of the solid obtained by rotating the region enclosed by y=(x^2), y=6x, about the line x=0 can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower limit=a]________dy with limits of integration a=_______ and b=________Problem 12 The volume of the solid obtained by rotating the region enclosed by x=3y, y^3= x (with y>/=0) about the y-axis can be computed using the method of disks or washers via an integral V=∫[upper limit=b, lower limit=a]_______dy with limits of integration a=______ and b=_______Can I have detailed, step by step explanation for obtaining the answer of the following question? Let Y1 and Y2 have joint density function given by, f(y1, y2) =3(y1) ; 0 <= (y2) <= (y1) <= 1 or 0 ; otherwise Find Cov(Y1, Y2) and correlation coefficient(P).
- Problem 5A gas engine has been running in a closed garage, resulting in a CO level of 600ppm. Uponopening the door, turbulent mixing begins. If the door is 3m wide and 2m high, the garage is10m long, and eddy diffusivity is approximated to be 1m2/s, how long will it be before COconcentration has dropped to 100ppm, which is considered safe for brief exposure periods?Assume there is no advective airflow through the garage.Answer: 179 seconds (or 3 minutes) Use the formula of C(t)=C0 e-(D/L^2)tProblem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x about the line y=9 can be computed using cylindrical shells via an integral V=∫_______________dy (with lower limit of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________Problem 10 The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x about the line y=9 can be computed using the method of washers or disks via an integral V=∫________________dx (with lower limit of a and upper limit of b) with limits of integration a=_________ and b=_________ The volume of this solid can also be computed using cylindrical shells via an integral V=∫_______________dy (with lower limit of alpha and upper limit of beta) with limits of integration alpha=_________ and beta=__________
