For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21 Show E(XY)

Q: Let f(t) = 3t4 - 6t+ 3et. Then f'(t) =

A: To find f'(t)

Q: a.) If f(x)= sin(In(x* )), find f'(x). b.) If g(x) = 5x find g'(x). %3D .2 x +3

A: (a) Consider the provided function, fx=sinlnx3 Find the derivative of the provided function. Apply…

Q: h" (t) = sec? t – Vt, h(0) = -3, and h'(0) = 3. %3D

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Q: The function z is defined by z(x, y) = x y-3 y Find A z and dz when x= 3, y= 5, Ax = - 0.04 and A y…

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Q: x²y" + 3ry – 24y = 0, y(1) = -8, y'(1) = –7. y =

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Q: Find y as a function of a if y(1) = 3, y'(1) = -7. y = r²y" + 3xy' - 63y = 0,

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Q: Knowing fli) = 3, f (1) = 27. find d (7) at

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Q: 4. Evaluate using Beta Function: B (6,5) a. b. {B}}})

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Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

Q: let it be 2= f(x,y) and Y=tan' () and X = === In (r²+5²) Prove that fxx+fxy= (y² + S) (fr+fso)

A: We have to prove

Q: Let F(x) =Cx41D, fCx)=X,and gox)=x+1 True or fals e (gof)(x) = FCX).

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Q: L=2-36X, y'co) =5, and ylo)=S x)

A:

Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern…

A: We have to find the differentiations of the give function and find y101.

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

A:

Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: Find y as a function of a if y(1)9, y'(1) = -5. y = x²y" - 15xy' + 64y = x²,

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Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: Q/ Let X be the r.v such that E (X) = 2 , E(X²) = 2a , E((2+ aX)²) = 2a³ %3D %3D Find the value of a…

A: It is given that, E(X) = 2, E(X2) =2a, E((2+aX)2) =2a3

Q: n For each nEN, consider x = with x ER+. Define the sequence {gn} by x (a) (b) A = [1,2) CR. (1)…

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Q: Find of the function f(x,y) = sin(x²y³). əx3

A: The product rule of differentiation : (PQ)'=PQ'+QP' sinx'=cosxcosx'=-sinxxn'=nxn-1 Use the given…

Q: Find f, (8,2) if f(x.y) = e* - 5y.

A: We can find the answer as below

Q: Let f(x) = In(x² – 14x + 52) f'(x) =

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: Suppose f, g have the following values: f(3) = e5 and g(3) = 2. ƒ'(3) 10 and g' (3) = = 8. 4 Let y¹…

A: To find the value of y' at (3,-3).

Q: 3/(a) Let X × b(n, –) and E(x)= E(16–7x) find n.

A: Solution : Given : X ~ b( n, 14 )             E(x) = E( 16-7x ) To find n : It is known that for…

Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

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Q: Determine the NATURAL cubic spline S(x) that interpolates the data f(1) = 1, ƒ(2) = 1, and f(3) = 0.

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Q: Let f(2) = (32² – 7)* ( – 7æ² + 8)² f'(x) =

A: