Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y].
(b) If X and Y are independent, then fY|X(y|x) = fY(y)
Q: 1.Suppose that the joint p.d.f. of Y, and Y, is defined by: e-Y1/y2 · e-Y2 0 < y1 < 0, Y2 0 < y2 < ∞…
A: Given: The joint p.d.f of Y1 and Y2 is defined by:
Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.
A: Click to see the answer
Q: that X and Y have joint pdf f(x, y) ={x + 3x^2y if 0 <= x <= 1 and 0 <= y <= 1, 0 otherwise. (c)…
A: From the given information, Consider, the Joint pdf of X and Y is as follows: fx,y={x+3x2y if…
Q: Show that the function f(x,y) =x² cos² y+ ysin² x+xe" , satisfies the 2 COS Lipschitz condition in…
A: Click to see the answer
Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1
A: Click to see the answer
Q: Let f1(x, y) - e cos(5y), f2(x, y) = x² – 25 y². Find Vf, and Vf2, and show that %3D (fv) = 0 for…
A: Click to see the answer
Q: Let W=x*yz.compute the differential dw.
A: Click to see the answer
Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…
A: First method r=x2+y2r=(α cost)2+α sint2 since x=α cost and y=α sint =α2cos2t+α2sin2t…
Q: If U(x, y) = -e-Y sin x andf(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = %3D Select one: ey…
A: Click to see the answer
Q: Z and dy 없 of y%3 (5x2 - ) (cos ar d²y Determine (cos x + In x).
A: Click to see the answer
Q: F(x) = x · S, 2e' cos-lt dt at x = 1 In x
A: Click to see the answer
Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…
A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.
Q: Q7 Show that CX,y) =e is Condinuous at co,0)
A: The given function is: fx,y=e-x2+y2 The given point is 0,0
Q: Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D
A: use partial differentiation for finding the derivative.
Q: f(x) = In(2 + cos x). -2.125, xk+1 = Ik +0.5, yk = f (xk), k E N To = %3D %3D = 0r
A: The function is fx=ln2+cosx Conditions: x0=-2.125, xk+1=xk+0.5, yk=fxk, k∈ℕ xk+1=xk+0.5…
Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.
A: Click to see the answer
Q: Verify Young's Theorem y? x2 z = In(2x + y) + +e(x+2y) y
A: Click to see the answer
Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…
A: To find Partial derivatives of the given functions
Q: Find the total differential. w = e3y cos(5x) + z5 ||
A: Click to see the answer
Q: Let f(x, y,z) = z-sin(xy), x = t, y = ln t , z = e^(t-1) . F
A: Click to see the answer
Q: Find a homogeneous (linear) DE with a following FSS: y1(x) := 1; y2(x) := sin(5x); y3(x) := cos(5x)
A: Click to see the answer
Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…
A: For the given vector function to be independent, it must be derived from a potential scalar function…
Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy
A: Click to see the answer
Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-
A: Click to see the answer
Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2
A: Click to see the answer
Q: g(x) [1 – sin(re')] dt In x
A: Click to see the answer
Q: ду Let y = In Vx² + 2z3 + cos(b³), find
A: Click to see the answer
Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|
A: Consider, f(x, y, z) = ln(x² + z) +…
Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.
A: Click to see the answer
Q: Let F(x,y,z) = z* + x+ y sin x + x In z 0, where z fx.y), then at (0,0,1) and are dy equal to: ax
A: Click to see the answer
Q: B. Let z- ( x-y)e×y (x-y)exy Show: Zxx + zyy + exy Cya-x3)= -z (xy+ 2)
A: Partial derivative of a function z=f(x,y) with respect to x is the derivative of z keeping y…
Q: Let {yk } be the DFT of {x; }, where x = [0, –1, 0, 1] y3 = O i -1 -i 1
A: Here, x0=0, x1=−1, x2=0 and x3=1 We have to find y3 Now, y3 is given by…
Q: 1: تحقق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ب 3 fxxy2 ل لدالة : f(x, y,z)…
A: See the attachment
Q: If f(x.v)= e-2x° cos(5x +y),- af dy O a. e-2[4xcos(5x +y) + sin(5x + y)] O b. -e-2x[4xycos(5x + y) +…
A: Click to see the answer
Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)
A: Click to see the answer
Q: Let f(x,y, z) = In(x²2+ z) + y²e*z – cos(2yz). Find fzyx·
A: Click to see the answer
Q: 23. Given that f(0) = v2 cos (e-), the minimum value of o1+ v2 C. %3D COS D.-1 A. V2-1. B.2N2
A: Since you have posted multiple question in this question so I have solved first question as per our…
Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…
A: Click to see the answer
Q: Find the critical numbers of the function. b) g(x) = |2x + 3|| c) f(e) = 2 cos 0 + sin2 0 d) f(x) =…
A: gx=2x+3 fθ=2cosθ+sin2θ fx=x lnx
Q: Let {yk} be the DFT of {x;}, where x = [0, –1, 0, 1] y3 = O i -1 -i O 1
A: DFT of xj, where x=[0,-1,0,1] We have to find y3 Here, x0=0, x1=-1, x2=0, x3=1 By using,…
Q: Let z = = g(x, y) = e* cos y +y In(x – 1).
A: Let we havez=g(x,y)=excosy+yln(x-1)If x=s-t and y=s2-t2
Q: If Z = f(xy) + g). Prove that; x2· Zxx + x · Zx = y² · Zyy + y· Z,y-
A: Click to see the answer
Q: Let y = x. Find dy and Ay at a = 8 with dx = Ar = 1. dy Ay =
A: Click to see the answer
Q: HW.8. Use farseval's theorem to find if f(t)=A e-alti Ans: A?
A: Click to see the answer
Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find
A: Click to see the answer
Q: If z = sin(xy), then dz is A y cos(xy)dx + x cos(xy) dy y cos(xy) + x cos(xy) dy C y cos(xy)dy + x…
A: z= sin(xy)
Q: Solve the DE X"y'+x°y= - csc(xy) by forming integrable combinations. 2x²cos(xy) = Cx2 -1 B 2x2…
A: Differential equation
Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…
A: ddxsinnx =cosnxddxnx =ncosnx
Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)
A: we will find the derivative of given function using basic differentiation rules.
Q: If z=x+iy=r(cos(0) + isin(e))then
A: The given equation is z=x+iy=rcosθ+isinθ.