If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

Q: Calculate the total differential of: a) z = 3x² + xy-2y³ b) z = c) z = x+y 2xy x+y

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: find a unit normal vector UN to the curve y = x at the point p(1,3)?

A: The given curve is y = x3, we can write it as x3 - y = 0 = f(x,y,z), where z = 0

Q: X, X2 ixd.u Co1) yi= Xi+X2 ェニメルナメ」 %3D d distribution

A: first consider the joint density!!

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Q: Consider the joint PDF fx)(x,y) given in the following. Let W=X+Y. fx,y(2,y) = Sc(2x+y), 0< z< 2, 0<…

A: From the given information, the joint pdf for X and Y is, The value of c is obtained below:…

Q: Compute the partial derivatives: = Z +y? || ||

A: Partial derivatve is

Q: Find the linearizations of the functionsat the given points. ƒ(x, y, z) = √2 cos x sin ( y + z) at…

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

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Q: Find the first partial derivatives with respect to x, y, and z. 3xz W = x + y dw %3D aw ду aw az %3D

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Q: e modulus valu

A: In the given question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: 2. Calculate the divergence of D = (÷)[10xyzảy + 5x²zãy + (2z3 – 5x²y)ã,] at P(-2,3,5).

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Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2).

A: Please check step 2 for the solution.

Q: Let X, Y ∼ U(0, 1) and X and Y independent. Find the PDF of U = min(X, Y ).

A: Find the distribution function of u and then pdf

Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: Find the partial derivative. f(p, q) = ev af

A: From the given problem; fp,q=e6pq As we know that: The chain rule: fgx'=f'gx·g'x The Power rule:…

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A: Concept: A vector is a directed line segment whose length is the magnitude of the vector and with an…

Q: Let Y1, Y2,..., Yn N(µ, 4), where is the unknown parameter. Find the MVUE for µ².

A: Fisher-Neyman factorization theorem: Suppose X1, X2, …, Xn is a random sample of size n taken from a…

Q: Find the first partial derivatives with respect to x, y, and z. 5xz x + y aw ax dy aw %3D az

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz W = x + y aw дх aw ду aw az ||

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Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +

A: Answer:-  Given that, X and Y have jointly Gaussian distribution.

Q: Find the orthogonal trajectories of the families of r e, where a being a parameter. (0)

A: Orthogonal trajectories are another family of of curve which are perpendicular to the the original…

Q: Compute all four first order partial derivatives of g(w, x, y, z) = sin(wxy) + e ^xyz .

A: The partial derivative involving multiple variables is obtained by taking one variable as the medium…

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

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Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: Use the full differential to calculate an approximate modulus value. of the vector (5, 8 ; 3, 1 ; 2,…

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Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

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Q: (i) Find the conditional pdf's fyx y and fyly y

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Q: Calculate moment generating function of J = Y + Y2 + Y3 to determine distribution of J and its %3D…

A: Given that Y1, Y2, and Y3 are independent geometric random variables with parameter p.

Q: =. Let X, Y and Z have the joint pdf x² + y? + z x2 + y? + z2 (2т) 3/2 1+ xyz exp exp where -o < x <…

A: The joint density pdf of X, Y and Z is, fx,y,z=12π32e-x2+y2+z221+xyze-x2+y2+z22 Consider,…

Q: find the derivative of f(x, y) = x² + xy at P,(1,2) in the direction of the unit vector u = i+ V2

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Q: Find the first order moment of pdf f(x) = (X^2)(x)[e^(-^x)], x 2 O, and O elsewhere. O /2 2/A O…

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Q: Find the symmetric equations for the normal line LN to the surface S:f (x,y) = 5VT +y? at the point…

A: Given function is S:fx,y=5x2+y2. We have to find the symmetric equation for the normal line LN to…

Q: find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)

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Q: Detemine whether the differential egualion is linear or hon linear and que reqsons. 2. Ody +sdy +Gy=

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Q: Find all the second partial derivatives of Z; given: a) Z = xy³In(3XEY )

A: The given function is, Z=xy3ln3xey Determine the first derivative of Z with respect to x.…

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: Find the first partial derivatives with respect to x, y, and z. 3xz w x + y aw dw %3D ду aw az ||

A: A detailed solution is given below

Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated  problems.These…

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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Q: The functions cos r and cos- are linearly dependent (0, ) on

A: evident from the two curves that after zero in a positive direction the two graphs coincide with…

Q: 4. Show that the covariant derivative of the metric tensor vanishes: V,gjk = V,gk = 0.

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Q: 05-Let X and Y have the joint PDF as fxy(x, y) = 2²e-1(x+y) where x> 0, y > 0, > 0. Find the…

A: INTRODUCTION :  Joint Probability density function: Let X and Y are any two continuous random…

Q: Use chain rule and compute dx/dv if z=x2+xy3, x=uv2+x,w3, y=u+vew

A: Here, the given functions are: z=x2+xy3,x=uv2+w3,y=u+vew So, z is the function of x and y and x,y…

Q: Find the derivative of alpha of t if alpha of t is the measure of the angle between the two given…

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Q: Find the first partial derivatives with respect to x, y, and z. 3xz w = x + y aw ax aw ду dw az

A: To find the partial derivatives of the function

Q: Find both first partial derivatives z = cos(10xy) dz %3D dx az ду %3D

A: We can find the partial derivatives as below

Q: What does Peanos EU theorem guarantee for the IVP:  dy/dt = -t/y ,  IC: (to,0)

A: Peanos theorem: "Consider the initial value problem y1= f(t,y), y(t0)=y0. Let f: Domain f →Rn. Then…

Q: Suppose that r is the position vector of a particle moving along a plane curve and dA / dt is the…

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Q: Find all partial derivatives of w = x sin(yz) – z In(xy)

A: To find all the partial derivative.