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Q: Evaluate f(x, y, z) dV for the function f(x, y, z) = xz² and region B = [0, 3] × [5, 7] × [4, 5].

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Q: Evaluate the line integral [6. 6ayⓇ ds, where C is the right half of the circle x² + y² = 4.

A: To evaluate :   ∫C6xy6ds, where C is the right half of the circle x2+y2=4 Prerequisite : We can…

Q: Find the value of kurtosis and describe the peakedness or flatness of the curve. Class Interval…

A: Concentration of all the values around the central value of the given data is known as measures of…

Q: Hiw Enadunte SSS where s is the selid bounded the Śur faces

A: Given - S is the solid bounded by the surfaces x2 + y2 = z2, z = 0, z = 1 To find - Evaluate ∭Sx2 +…

Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: show that a best critical region for testing H : 0 = 1 vs Ha : 0 = 2 is C = ((11, x2, ..., n) : c <…

A: The Neymann-Perason Lemma will be used to find the best critical regiol for given hypotheses.

Q: An area of a region bounded by a curve y = f(x), x axis and lines x = a and y = b for (b > a) may be…

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Q: (b) A point P with coordinates (X, Y) is uniformly chosen from the unit disk D = {(x, y) : x² + y² ≤…

A: As according to the guidlines we can solve only one question please post the other question…

Q: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

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Q: Define the Rolle's Theorem?

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Q: non -CentYal moment for An B (u,p) ECx³)?

A: Given; X~Binomial(n,p)The probability mass function of X is given by;P(X=x)=nxpx(1-p)n-x,…

Q: he area bounded by the curve y = 3Vz and the lines z = 5 and z = 9 above the r – aris is_ quare…

A: Find the area of bounded curve with line x=5 and x= 9 above x-axis

Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

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Q: dz; |z – i| = 1 (z – i)3

A: We have to use the Cauchy integral formula to evaluate the following integral ∮ ez2z-ι3dz over the…

Q: PewHite F in sphethal cordmates and compute its diergence.

A: The divergence of F is 3

Q: Let (X,Y) is a two-dimensional random variable with the pdf f(x,y) = {* +y 0<x,y<1 elsewhere Find…

A: Given: The probability density function of the random variable X and Y is given as:…

Q: ofind the Veelles Such that of A ond R

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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: It G acts set tdansikivey then show that y Salgdnap Hof 0n A by to the actioh af en A fusthus then…

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Q: The inturval of sunserge of ie ar0,2) -20)

A: We have to find out

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

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: byparts VE tan! (VE) dt

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Q: Let C1 be the line segment from (1,0,1) to (0,3,6). Evaluate dx + dy + dz.

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Q: 10. Para resolver la siguiente ecuación diferencial: y" + 2y' + y = 0 con y(0) = 1; y'(0) = 1 Se ha…

A: The solution of differential equation is given by using Laplace transform and partial fraction…

Q: Suppose there is a random vector (X, Y) of density f(x, y): 10<x<3y³€ • Find E(Y|X) • Find…

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Q: whelher Y+ vist diverges caer Convavayes Determine 一 tby using. test ist grat 2y [Inv

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Q: biveniJN/AN, Dis the midpoint of JA Prove: AJON E A ADM A.

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Q: j ula,0) =f(2) solue (4 Us ing neumann Boundary Conditions o lg Periodic Boundary conditio, usile

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Q: f(~iy)= ve 1, fund warginal olistribution for 2. Fud conditimal pdf tos, s) o. Estmato (osyei / xo)…

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Q: nstate Taylor's s theorem, giving the explivit foraula afn the ertor.

A: Taylor theorem related problem.....

Q: compule the W a M the veter field the perametenísed jind ni t yÏ and s is orientked doeunward o…

A: Now, we have to calculate the parts of integral and then put it in the integration.

Q: Find the region bounderd ABOUE ly ther pauabola X= (y-2 and bounded kčlana by anothen panaivic Iy…

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Q: g) div(7) for 7(x, y,z) = xyi + yz²j +x²yzk h) curl(ï) for ū(x, y, z) = xzi + xy²j+y²zk

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Q: 2) Find Ow/ôu and ôw/ôv for w= xy+ yz+ xz, x=u+v, y =u –v, z = uv at the point (u, v)= (1/2,1). 3…

A: If w=f(x,y,z) and x=g(u,v) ; y=h(u,v) and z=t(u,v) then, ∂w∂u =∂w∂x.∂x∂u+∂w∂y.∂y∂u+∂w∂z∂z∂u  and…

Q: Calculate (y+z)dx+ (x+ z)dy+ (x+y)dz , where C consists of line segments from (0,0,0) to (3,2,4) and…

A: We will use parametric equation of lines to find the integral

Q: If C is the line segment from (1, 4, 2) to (3, 2, 1), evaluate the line integral y+ 2) ds.

A: Express the line segment in its parametric form and then use the formula below to evaluate the line…

Q: J uore program Use a soft groping of ality aith motrix copobilities to'find the eligenualves the…

A: For any matrix, A , the eigen values are calculated by solving the equation, det(A-λI)=0 . Here , I…

Q: 16. Evaluate * :- S S $6(x² + y² + z? )dV В where B is the ball with center at the origin and radius…

A: (16).  We have to find the integral∫∫∫B 6x2+y2+z2 dV  ;      where B is the ball with center at…

Q: Let f(x) = e2sinx. Use the local linear approximation of fat x = 0 to approximate e²

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Q: When can we apply the Green's Theorem to compute circulation in R^2? O Curve C is simple and closed…

A: Note that Green's theorem works only for the case where C is a simple closed curve.  Further notice…

Q: 3 wtx

A: Solution:GivenTo find the integratonLetI=∫csc2x(1-3cot x)2dxFormula:ddx(cot…

Q: H-S Integrate the fallswing funCtini aver the given regionr. R: is the triangle cut from the first…

A: Evaluation of the integral

Q: Evaluate the line integral ∫Cydx+xdy where CC is the parameterized path x=t^2, y=t^3, 2≤t≤4.

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Q: 01. Evaluata the intenral and check your differentiating by antwer Gsin (a) + cat Ca)cscla) de= +C

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Q: Exz Let X, Xz, ~Xn be a random sample from Hhe 'parametter a Peisson distribu tiên with Estimate 1.

A: Poisson distribution: A random variable X is said to have Poisson distribution with rate λ if its…

Q: ral by making an appropriate change of variabl re R is the region enclosed by the lines y = 6x

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Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…

Q: =) Veaity gren's theorem fintegral So (zy'tat 3ndy) bound ay of dosed and y-m to evaluale line whee…

A: Firstly we use green's theorem to calculate the integral. ∫P dx+Q dy=∫∫RQx-Pydy dx∫2y2 dx+3x…

Q: Use an appropriate local linear approximation to estimate the value of the given qua

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