The joint density function of Y₁ and Y₂ is given by (30₁₂², (0, f(Y ₁¹ Y₂) 9/16 (a) Find F (11) 2 1 (b) Find F 2 T F( 12/1, 4). = (c) Find P(Y₁ > Y₂). 21/32 ₁-1≤ y₂ ≤ 1 – Y₁, 0 ≤ Y₁ ≤ 1, elsewhere.

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

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Q: The joint pdf of X and Y is given by fxy(x, y) =e (x+y), x>0, y>0 ind the pdf of U: X + Y 2

A: The joint pdf of X and Y is,It is required to find the pdf of A joint pdf for two variables…

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Q: х Set F(x) = (1 – t) dt. Find F'(4). %3D /1 F'(4) = -3 Find the average value of F'over [1, 4]. 4

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Q: Assume that f is a de ferentiable function with fax (5,0) =6 and fu(5, )=4. Let w Cu,v) =f (x (u,v),…

A: Given,w(u,v)=fxu,v,yu,vx=6 cos u+5 sin vy=7 cos u sin vfx(5,0)=6 and fy(5,0)=4 To find:wuπ2,π2

Q: (2) Evaluate 6y dV, where E = {(1, y, 1) | 0 < z < ry, 0 < y S 1, 0SISY} %3D

A: The objective of the question is evaluate the integral.

Q: So If fis continuous and f(x) dx = 20, evaluare let U = 3x f² f(3x) dx.

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Q: 3zyz f(x, y, z) = e %3D fz fy = f =

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Q: Find the following for z = f(x, y) = x? +5x2y3-y. az %3D ax

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Q: 6. Show that f(x) = sin x is uniformly continous on R.

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Q: The joint pdf of X and Y is b) Determine fx|y=0.5(0.1) fx,y(x, y) = 3 0 0<x<2, 0<y<1 otherwise

A: Given that  Joint pdf of X and Y is  fX,Y(x,y) = (x+y)/3   , 0 &lt; x &lt; 2 , 0 &lt; y &lt; 1

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Q: Let X and Y have the joint PDF f(x,y) = 2e−x−y for 0<x<y<∞. Find the joint PDF of Z = 2X and W = Y −…

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Q: Find the total derivative of f(z, y) = xy+3y² is a. df = ydx + dy b. df = ydx + 6edy C. df (a +y)da…

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

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Q: Let X and Y have the joint pdf f(x, y) = (1 – xy), 0 < x < 1, 0 < y < 1. Find E(X).

A: The given joint pdf is fx,y=431-xy,0&lt;x&lt;1,0&lt;y&lt;1.

Q: 2. Suppose that X and Y have joint pdf given by f(x,y) = kx, 0 sx<1, 0sysl-x Find a) k b) P(Y < X) )…

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