11) Let X, and X2 have the joint pdf (6x2 0 < x2 < x1 < 1 f(x1, x2) = - otherwise a) Find the marginal densities. b) Find fx1|x2 and fx2]x1 c) Find E[X2|X¡] d) Find E[X], E[Y], E[XY], VAR[X], VAR[Y] e) Calculate COV(X,Y) f) Calculate CORR(X,Y)

Q: 1. Show (in terms of e- 6) that a function f : R* → R defined by f(x, y, 2) = (2x + 3y + 42) is…

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Q: (a) Show that y for the given z = e" In x+ xy

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Q: f (x, y, z) = ln(x2 + z) + y2 exz. Fin

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Q: 3. (a) Show all functions satisfying u"(x) = 0 are linear by integrating the expression of u"(x) %3D…

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Q: 2. Let X be continous with pdf f(x) = 1/x² if 1 < x < ∞, and 0 otherwise. (a) Does E(X) exist? (b)…

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Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: 2. A college professor never finishes his lecture before the end of the hour and always finishes his…

A: Note: Since you have posted a question with two subparts, we will solve the first part for you.…

Q: Consider the function f(x) = ln(x)/x^5. f(x) has a critical number A = __? f"(A) = __? Thus we…

A:

Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: (c) f(x,u, v) = – log(uv - x" x) on dom f = {(x,u, v) | uv > x² x, u, v > 0}.

A: C.

Q: 1.Test the function def ined by f(x.y)=xlnx- ylnx for its homogeneity. If it is homogeneous, give…

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Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

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Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 6.5.4 Find the PDF of W = X + Y when X and Y have the joint PDF fx,x(z,y) • otherwise.

A: Given: The joint probability density function of the random variables X and Y is provided as:…

Q: The function f (x, y) = x3y + x2 + y2 − 2x − y + 4 has a stationary point (1, 0). Compute the…

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Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

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Q: (3) A study on optimizing revenue from a website considered dividing cus- tomers into two groups…

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Q: 1. Show (in terms of e- 6) that a function f : R + R defined by f(1. y. 2) = (2x + 3y + 42) is…

A:

Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: Show (in terms of e - 6) that a function f : [2,7] R be defined by f(z) = V² +1 is uniformly…

A: In this question, we need to show the given function f(x) is uniformly continuous.…

Q: (a) Find the marginal PDFS fx(x) and fr(y). (b) What are E X and Var X? (c) What are EY and Var|Y?

A: Provided information is, The random variable X and Y have joint PDF as: fx,yx,y=x+y3      0≤x≤1=0…

Q: Find the linearization L(x) of y = e5* In(x) at a = 1. L(x) =

A: Given that:y=e5xln(x)a=1To find the linearization

Q: If Σ α An diverges then E ca can diverges only if c > 0 only if c < 0 only if c+ 0 for any real…

A: Given, ∑an diverges then find for which values of c, ∑can diverges.

Q: 1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t…

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Q: Verify Young's Theorem In(2x + y) y2 x2 + + e(x+2y)

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Q: 1. Show (in terms of e – 8) that a function f : R³ → R defined by f (x, y, z) = (2x + 3y + 4z) is…

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Q: [1] Show that the functions In x, In(x) are linearly dependent on (0, co)..

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Q: a. The function f: RR given by f(x)=x² is twice continuously differentiable in R", and its Hessian…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: 3) Consider a particle of mass m in a one-dimensional box of width L. Apply the variational…

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Q: 5 The function f (x, y) =| x² cos² is homogenous in x and y of degree,

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Q: 12 - Find an upper bound for the error |E(x, y)|in the standart linear approximation of f(x, y) = x²…

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Q: 7. Let f(x, y) = In(x)+2 ln(y) – x – 4y. Find the critical point of f and determine if it is a local…

A: Let's find.

Q: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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Q: 15. Let f(x) = x² -4x+3. What are the critical number(s)? x = 1 b. x = 3 c. x= 1 and x 3 a. d. x = 2…

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Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

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Q: Find the linearization L(x) of y = e3" ln(x) at a = 1. %3D L(x) = ||

A: See the details solution in the details solution

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 3n/2 %3D

A: We have to find the linearization L(x) of the given function.

Q: 4.18 Given that g(x) > 0 has the property that 6. show that is a pdf. f(x, y) 2g g(x) dx = 1, (√x² +…

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Q: 3.2 Let f(x) = Approximate the integral x4 x L f(x) dx using the Trapezoidal rule with n = 4. -2

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Q: 1 3. Integrate the function f (x, y) = over the region bounded by x-axis, line x = 7, and the curve…

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Q: Find the critical number(s) of the .4 * (function f(x)=In(2x)/(3x )2 نقطة( In(2x) f (x) 3x e/2 and 0…

A: Calculus

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: 5 The function f(x, y) = | x' cos is homogenous inx and y of degree

A: Given that: f(x, y)=x2cos2yx-y2+x3y

Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

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Q: Find the linearization L(x) of y = e6« ln(x) at a = 1. L(x) =

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.