Q1: (a) Let the joint p. d. f. of X and Y is f(x, y) = {' find the p.d.f.of W = X + Y. 0≤x≤ y ≤ 1 e. w.

Q: Check it for f(x, y, z) = x²y°z*, that is, compute Vf first, then V x (Vf).

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Q: Let f(x, y) = xy – y³ + x². where u =. O A. 37 O B. -37 10 37 √10 O D. -37 C. Du(f)(1,2)=?

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Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: 1 Evaluate f fp2 f (x, y) dædy where f (x, y) (1+æ² + y²)?

A: A polar coordinate system contains a reference point and a reference direction. The reference point…

Q: Find the exact value of F. dr using any method. b. F(x, y, z)= C is the line segment from (1, 0,…

A: The given vector field is Fx, y, z=yz, xz, xy+2z. We have to find ∫CF·dr.

Q: • Given f(x, y, z) = x² In(x + y- z), find f(2,4, 5). а. 0 b. 1 с. 2 d. 3 O a. b. С. O d.

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Q: 21 - Let V = R3,S = 5 Show that = Span(S) %3D

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Q: Calculate , if xyz Ax, y,2) = x² – x²y³ -2 3 = x -x y -Z A.5 1 C. No one correct. В. D. E. 7 Е.

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Q: The student council is hosting a drawing to raise money for scholarships. They are selling tickets…

A: From the given information we want to find expected value of profit.

Q: ! Given a p.d.f. of a c.r.v. x as follow: f(x) = {3x² 0<x< 1 " 0. W y = 3x, then the p.d.f. of a…

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Q: S f(t) dx = 0. 1.

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Q: H.W 1- If P(X = 0) = 0.2, P(X = 1) = 0.3, P(X = 2) = 0.5, P(Y = 0) = 0.4 and P(Y = 1) = 0.6.…

A: Given: PX=0=0.2PX=1=0.3PX=2=0.5PY=0=0.4PY=1=0.6

Q: Let w = f(x, y) with f E C² and x =h – kh, y = 4k. Which of the following statements are true?…

A: To find  Which of the given statement is true.

Q: Let f(x, y) = x(y - 3) and F = Vf. If r = with 0 ≤ t ≤ 2, then [F. dr is equal to: a. -7 b. -11 c.…

A: We find the line integral in the following way

Q: Recall the relation between degrees Celsius and degrees Fahrenheit: F = 1.8(C + 32) X and Y are…

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Q: Let f(x) = VT, 9(x) = ,. , andh(x) = x². (h o ((h o go f) – f)) (4) = %3D 5-x Select one: a. 4. 81…

A: let f(x) = x , g (x) = 45-x and h (x) = x2f (4) = 4= 2g (f(4) = g2= 45-2= 43h (g(f(4)) = h 43=…

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

A: From the given information, W follows normal distribution with mean µ=-1 and variance σ2=4.

Q: Let f(x,y) = In ( x2 + y). If fy(2,a)=fy- 1, 2), what is the value of a? а. 3 O b.7 О с. 8 d. 6 O e.…

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Q: Let f(r) = 2. 1 + Find f(1/2) 1. Find the domain of f ii.

A: Given data is: fx=11-21+11-x Calculate the value of f12 and the domain of the function.

Q: Let f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 Oc. 0 Od.-2 e. 2

A: From the given problem:   fx,y=lnx2y   fx2,1=fy5,a   Now,   fx=∂f∂x=∂ ∂ xlnx2y=1x2y∂ ∂ xx2y=1x2y·…

Q: Let X and Y be independent and distributed as N(mu, 1). Is T=X-Y sufficient?

A: According to factorization theorem, if the likelihood function Lx,θ can be expressed in the form.…

Q: 5. Find the x-coordinates for all points of discontinuity for f(x)- 「X316, xśl x〉 1 2 c. 1, 32d.…

A: First we check the limits as x approaches to 1 from left side and right side .

Q: Let f(x,y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 O.0 O d.-2 O e. 2

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Q: a.Give the joint p.d.f f(x,y) if the 2 balls are drawn with replacement? b.Give the joint p.d.f…

A: As per the guidelines of Bartleby,we are giving here solution of first 3 parts only

Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: 12. Let f(z) =,h z 0. Then f(2 + h) – S(2) h A) – 4+ 2h 1 B)- 4+ 2h C)-- 4- 2h 4-2h

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Q: Find the pro ection of v on the line with equation

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Q: 6. Let f be function such that f(-a) = - f(2) for all If a %3D х. | f(2)dz = 5, then L2) +0)dz =…

A: With the help of definite integral property we solve this.