Let (X,Y) be random points chosen from the closed unit ball R<1 where R = X2 +Y2. • Find the CDF of R2 • Find the density for R

Q: Question Suppose the r.v. xy, z have a joint prob dersity Function given by; Flzy,z) =L(zty+241)…

A: Suppose the random variable x,y,z have a joint probability function given by; F(x,y,z) =…

Q: Let S be the surface of the solid hemispherical region above the plane z = 0 and below the sphere…

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Q: calculate the curl and Divergence A= xyzi-2r2lny +2yak at リ-ル1).

A: Given: A=xyz3 i-2x2z ln y j+2yz4 k              point is (1, -1, 1)∇.A=∂ ∂xi+∂ ∂yj+∂ ∂zkxyz3 i-2x2z…

Q: The region R lies on the lines x – y = 8, x + 7y = 8, x - y =| and x + 7y =

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Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Let F(x,y,z)=(4x-5yz, xy, z^2).  Calculate curl F.

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only the first…

Q: Find the average value of f(x, y) over the region R. f(x, y) = ex + y R: triangle with vertices (0,…

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Q: 9. Is Y = {(x,y, z) | y=z} R?? a subspace of

A: ψ={(x,y,z)| y=z}

Q: II. Let RVsx, Y be uniform on triangle with vertises (0, 0), (2, 2), (2, 2). Find 1. Joint pdf…

A: Note: As you've posted multiple questions, the first one will be answered as per our policy.Also,…

Q: Let T be the triangular region region with vertices (1,0,0), (0, 1,0), and (0,0, 1) oriented with…

A: The flow rate is just flux of velocity v=-16jm/sthrough the triangular surface. The equation of Ƭ is…

Q: Find the centroid of the region x² + y² + z² ≤R²,z≥ 0. (a) (0,0,³R) (b) (1,2, R 8 R 3 (c) (0,0,.²)…

A: The  given region is  which can be described in cylindrical coordinates as To calculate the center…

Q: FIND THE CENTER OF MASS RECTANGULAR LAMINA WITH VERTICES (0,0), (16,0), (0,6), AND (16, 6) FOR 2…

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Q: Find symmetric equations of the normal to the surface, r (u, v) = at a point (1, 1, 3

A: given ru,v=&lt;u2,v2,u+2v&gt; therefore ru=∂∂uu2i+∂∂uv2j+∂∂uu+2vk=2ui+0j+k…

Q: find laplace of f(x,y,z)=2x3y2z2

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Q: Let S be the portion of the surface z=Vy²+1+e* that lies above the region R= {(x,y)ER?:x²+y?s1,y20}…

A: Given the surface is z=y2+1+ex,and R=x,y∈ℝ2|x2+y2≤1,y≥0. Find I=∬SF·ndσ, where F=ye-x,2ex-2z,y.

Q: 6. W is the set of al twice differentiable functions f that satis fy yu+ 3y!+ ay= O 3 y'+ 2y=

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Q: Let T be the triangular region region with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1) oriented…

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Q: Find the average value of f(x, y) over the region R. f(x, y) = x² + y² R: square with vertices (0,…

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Q: Let F(x, y,z) = (-xe² +3x, -ye² + arctan(x? + z), 2e²) and S the portion of the sphere acoording to…

A: Given that Fx,y,z=-xez+3x, -yez+arctanx2+z2, 2ez. Also, S=x,y,z| x2+y2+z2=1, z≥0. To determine the…

Q: Which of the following is the moment of inertia about the x-axis of the plate object with surface…

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Q: Find the flux of F across S, 1.1. S F. N dS where N is the upward unit normal vector to S. F(x, y,…

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Q: Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal vectors,…

A: The given vector field is F = xy, 3xz2, yz. Our aim is to find the flux or surface integral of the…

Q: Let P be the portion of the tilted plane in R' parameterised by r(u, v) = ui + uj + vk where 0 < x <…

A: Given: To explain the correct option of the given statement as follows,

Q: Use Green's theorem for the work done by the force F= (x - y)i + (x + y)j, for the shaded region R…

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Q: Find the curl and also the divergence of F(x, y, z) = (x²z, e" + zz, xyz)

A: The objective is to find the curl and divergence of Fx,y,z=⟨x2z,ey+xz,xyz⟩ Curl and divergence of…

Q: Find the kernel of linear map L:R R given by L(x,y,z)%3D(0,z,y)?

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Compute the normal vector to the surface (u, v) = (u² - v², u + v, u-v) at the point (2,4) and use…

A: Given  The normal vector to the given parametrized surface at a point is the cross product of the of…

Q: b) Use the divergence (Gauss') Theorem to calculate the flux of F across S where F(x,y,z) = xye²i +…

A: Using the Gauss Divergence theorem we have to find the flux through F(x,y,z)=xyezi+xy2z3j-yezkwhere…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!