Problem III. Let X and Y be iid as N (0, 1) and let Z = -X if XY <0. 1. Derive the mgf of Z, if this exists. 2. Derive the pdf of Z.

Q: 4. Find a solution of the Bessel's equation of order zero.

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Q: 4. Suppose Y1, Y2 are independently and identically distributed with Unif((0,1)). Let Z = Y1 · Y2…

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Q: Problem 10: Over the circle X² + Y² sr?, random variables X and Y have the joint PDF Sx.x(z, v) = {…

A: (a). Find the marginal PDF fX(x): The marginal PDF fX(x) is obtained as given below:

Q: Question 3 a) Develop a first order method tor for approXivaating t' (x) which uses the data f…

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Q: In Problems 11 through 18, find the position function x(t) of a moving particle with the given…

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Q: QUESTION 11 Let X denote the time to failure (in years) of a certain hydraulic component. Suppose…

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Q: 18 0-17 ¹8 cos(x¹8+18) Question 6 Find the total differential for the function w = Odw - 262³ y sin…

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Q: Consider the differential equation dx/dt = x + kx³ con- taining the parameter k. Analyze (as in…

A: Given differential equation,dxdt=x+kx3

Q: QUESTION 12 Let X denote the time to failure (in years) of a certain hydraulic component. Suppose…

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Q: Discuss and derive the following 1“ integral equation, a): ure = 1

A: we know that length of ℓ = rθ  ℓ / 2πr=θ / 360 so from this, we can prove that  ℓ =rθ

Q: 1. Compute E(1/X) 2. Find the cdf and the pdf of Y = 1/X 3. Compute E(Y) and compare this result…

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Q: Question #: 5 An inventor claims that her new device will "drastically reduce" the oil consumption…

A: (5) Given Information: An inventor claims that her new device will drastically reduce the oil…

Q: :. Foum dhe Þeatial differential equalion arbitary furetion) Z= y2+2F(* logy) (loy eliminating the

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Q: În Problems 2 to 9, use Laplace transforms to solve the given differential equations. d?y dy - 24-…

A: Given that, 9d2ydt2-24dydt+16y=0  with, y0=3  and y'0=3 Taking Laplace Transformation on both side ,…

Q: 5. The motion of a mass attached to a dashpot and a spring as it experiences a force can be…

A: Given differential equation is  md2xdt2-Bdxdt-kx=1    , m=1, B=1, k=6, x0=0, x'0=0⇒d2xdt2-dxdt-6x=1…

Q: [2.73 Find a general Solution of following monhomogeneous limear 1ogeneous linear ODE g+ +1+#)は = e…

A: non-homogeneous differential equations

Q: 2.3.8. Let X and Y have the joint pdf f(r, y) = 2 exp{-(x+y)}, 0 < r < y< ∞, zero elsewhere. Find…

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Q: 1- Problem 4: B) Estimate the following integration with n = 4 using Trapezoidal rule and find the…

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Q: 15. Use differentials to approximate V143.7

A: Use of differential

Q: 2 4 Find an equation of the normal line to the curve 3x¯y' – x°cos(ny) + 4x + 2 = 0 at the point…

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Q: 7:31 MAC2311C-FINAL-A PDF - 234 KB 10 Problem 10. The value of the integral nz dx equals: (A) In 2…

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Q: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý -ye

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Q: Problem 21 Given the equation xy=12, set up an integral to find the length of path from x=a to x=b…

A: We first write the given function as y= Then we find dy/dx

Q: 2. J Jx3+3 dx PROBLEM SOLVING. In problems 1-20, find the most general anti-derivative. 1. So² –…

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Q: PROBLEM 9 Two random processes are defined as X (t) = A. cos (ot + 0); Y (t) = A - sin (Qt + 0),…

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Q: Problem 2. Find the general family of antiderivatives for each of the two given func- tions. 1 (a)…

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Q: 2+ Problem 3/ Evaluate z*dz along the line y=

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Q: Problem 2 Let X be Uniform(0, 1) and Y be Exponential(1). Assume that X and Y are independent. i.…

A: Given problem is :

Q: Problem 1. Let f(x) = c/x – 4 on [5,8] Find c so that f is a pdf. Determine the mean. -

A: Given: f(x)=cx-4       5&lt;x&lt;8 As f(x) is pdf : ∫58f(x)=1∫58cx-4=1∫58c(x-4)0.5=1…

Q: Problem 2 Let X be Uniform(0, 1) and Y be Exponential(1). Assume that X and Y ar independent. i.…

A: From the given information, X~U0,1Y~Exp1 X and Y are independent. The joint probability density…

Q: Question 15 Write a chain rule formula for the following derivative. for w = f(x, y, z); x = g(s,…

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Q: Problem 5-1 Evaluate the given integral f(x) dx

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Q: Problem 1. L(x) = In 1.05 Find the linear approximation of f(x)= In x at x = 1 and use it to…

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Q: Problem 18 Evaluate the given indefinite integral.  ∫ (3-5x(e^x))/(x)dx=

A: The given integral is

Q: Sheet 4 Numerical analysis dx QI/ Evaluate Jo 1+x2 Simpson's 1/3 rule Simpson's 3/8 rule i- ii-

A: In the question we have to find value of integrals.

Q: Solve the following heat flow problem:

A: Given,            ut=3uxx, 0&lt;x&lt;π, 0&lt;t&lt;∞                ...(1)u(0, t)=u(π, t)=0,…

Q: Question# 3: Two random variable X and Y have the joint PDF given by: 2 e-(x+2y) ,0 < x < 0,0 < y <…

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Q: dy Vy; y(0) = 0 dx

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Q: Problem 2. Let Mx(t) =e+et +et. Find the following: (1) E(X). (2) V (X). (2) Tho probobility mass…

A: Given mgf is, MX(t)=16et+26e2t+36e3t 1) E(X)=ddxMX(t)|t=0        =16et+46e2t+96e3t|t=0…

Q: Problem 4. Let f : R –→ R be a twice differentiable function. Consider the first order differential…

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Q: Problem 6  Suppose  f(x) =∫(36-t^2)/(4 + cos^2(t)) dt Upper limit of integration= x Lower limit of…

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Q: Question 2 Let joint pdf for X and Y as follow: f (x, y) = *(2-y) 4 for 0<x<2 and 0<y<2 a) b) Find…

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Q: Question 5.1 Y,,Y2, .. Yn are n iid observations of Y-N(u = 0,0). µ is known to be zero and o is…

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Q: In problem 17 and 18 estimate x*dx using: 17) The trapezoid rule and n=6 18) Simpson's rule and n =…

A: We have the integral ∫03x4dx. For (17), Trapezoid rule: Average of Left and Right Endpoint…

Q: EXAMPLE 4.4 Ans: 3 Given the following data: -1 3 y3Df(x} Approximate f(2) by using Newton's divided…

A: We approximate f(2) by using Newton's divided difference interpolation.

Q: In Problems 11 through 18, find the position function x(t) of a moving particle with the given…

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Q: Question 18 Using differentials, approximate v 9.1 A) 3.01666667 B. 3.017654314 3.016620626…

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Q: 1: The wavefunction for a particle that is confined to 0 sxS0.3 is: 4(x) = e. Find the normalised…

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