Two students are named to present their work from a class of 12 students: 3 from electrical department, 5 from telecommunication department and 4 from computer department. Let X denote the number of chose electrical students. and Y is the number of chose telecommunication students. Find: a. Px.y(x,y) b. ЕТX] c. P(Xs 1|Y< 1) с.

Q: If  x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 2.  (Enter your answers as a…

A: Solution: the objective is to find dy/dt

Q: 9. If f(x, y) = x³ + 4xy² + y3 %3D show, that f (ax, ay) = a³f (x,y) %3D

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Q: Find the line of best fit for x: 2 2 68 10 y: 01233 O ŷ= 0.344x+0.125 %3D O ŷ = 1.29x - 3.14 %3D Oŷ…

A: The regression is a linear relationship between one dependent variable and one or more independent…

Q: a of the following juncions. s- 1 (b))F(s)% = %3D 2s2 -8 s + 11

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Q: "he pmf of X is 4.x – 1 - fx(x) = where x = 1, 2, 3 %3D %3D to

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Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

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Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: 4,5 f (x,V)= Sx"y%,compute fx and fy

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Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: Prove that in the pairs of positive numbers ¤, y for æ² + y° = r the sum a+y is greatest when z = y.…

A: Here we solve the given problem of calculus.

Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

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Q: Use the modified Euler method of Lecture 3, with n 10, to find xt1 = -t, (0) = 0

A: Consider the given differential equation.

Q: Given F(r, s, t) =r(3s² + 9t°), compute: Frst

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Q: f(z) =z2 is discontinuous in C

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Q: Use the fact that 9(z) dz 65 to compute each of the following: g(y) dy = %3! | 9(z) dz 9(z) dz %3|…

A: We use definite integral properties

Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: Use the linear approximation (1 + x)k = 1+ kx, as specified. Estimate 1.012.

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Q: Given F(r, s, t) = r(3s² + 3t²), compute: Frst

A: Solution of question is written in below steps.

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

A:

Q: Consider f(x, y) = x³ + 2ry + y. Compute the following: (b)

A: Answer and explanation is given below.. Simply do partial derivative with respect to x and y.

Q: If f(x, y) = 8xe2y + 8y Inx, then is given by:

A: The given function is: f(x,y)=8xe2y+8y ln x Now, ∂f∂x=∂∂x8xe2y+8y ln x       =8e2y+8yx

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: For æ > 0, 1 dt 1+t2 A 2/7(1+z) B 2/7(1+JE) c) 1+1 D 1+z E VE

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Q: The DE : y' =e3x-7Y is seperable Select one: O True False

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Q: 2. Determine Var(Y) when Y 3X1 +2X2 with Var(X1) 1, Var(X2) 5, Cov(X, X2) 2, E X1} 3, аnd E{X} 4.

A:

Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: 3 - If h(x, y) = y – xy – x2, find at the point (2, n) ду

A: The given function is hx, y=y-xy-x2 and the point is 2, π.

Q: 3. Vsech 2t Evaluate dt 3. coth 2t

A: Application of integration

Q: Express E: livenr coumbination of Ÿ; = and V as a

A:

Q: b) Find if f(x, y) = ysin( xy)

A: Givenf(x,y)=ysin(xy)find ∂w∂t

Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

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Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: Let z = 3x*y, find Vz.

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Q: two variables are independent, each with the pmf given in the accompanying table (so X,

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Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: 2t (t - 7 dt

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Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: 3. Find and at (0,0) where if (r, y) # (0,0) if (z, y) = (0,0) f(1, y) = Are they equal?

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Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: Suppose that z = f(x,y), find for 4 x²z* – 5yz³ + xy? - 3z? = x

A: Given: 4x2z4−5yz3+xy2−3z2=xz=f(x,y)∂z∂x=?

Q: Find dr. J (1+z²)3/2 - In Vx² + 1 + x| + In |Vx² + 1 + x| - Ja? + 1 +c Vx² + 1 O Option 3 Option 1…

A: Let I= ∫x21+x232dx Let x=tanθ ⇒dx = sec2θdθ Substituting this in I, we get

Q: Let f(x, y) = x² + y2 + 2x + 4 and P,(-1,0) then Vfle, is i – j. True False

A:

Q: :) Suppose X1, X2 ~ Uniform(0,2) are independent and Y =2X,+X2 . Find P(Y < 2). h:1:

A: c) Given that X1,X2~Uniform0,2 are independent. The joint probability density function for X1 and X2…

Q: Calculate az/ax, where xez + zeY = x + y.

A:

Q: Use cubic interpolation method with two points to find uz , where a = 0. 6, h 0.1, ɛ = 0.001 and O'…

A: Cubic interpolation method gives the following formula for evaluation, For, μ2=a(∅')-h1+∈ Therefore,…

Q: Let flt.v) = v+3t°e'. -2 -y + 3t2e'. Then f satisfies a Lipschitz condition in y with L = 2, given…

A: