68 Let the 2-dimensional random variables (X, Y) have joint uniform density functionf(x,y) = ²,0≤x≤3, 0≤y≤2.65. Find the joint moment generating function of (X, Y) given byMx,y (t₁, t₂) = E[e¹₁X+t₂Y] = √∞ Set₁X+t₂Y ƒ (x,y)dxdy.6. Find the moment generating function of X given byMx (t₁) = Mx,y (t₁,0) = lim Mx,y (t₁, t₂)t₂→07. Find E[X] and E[X²] from Mx (t₁).

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Answered: Let the 2-dimensional random variables…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)
Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. FInd (d) fZ|XY (z|x,y), (e) fX|YZ(x|y, z).
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Let (X, Y ) be a random vector with joint density function of the form:f(X,Y )(x, y) = 24xy, 0 < x < 1, 0 < y < 1, x + y < 10 , otherwise(c)Compute the conditional probability P(X < 1/6|Y=1/2) and the conditional expectation E(X | Y = y)
Use the rejection method to generate a random variable having density function f(x) = kx1⁄2e−x , x > 0 where k =1/Γ (3/2) =2√π
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Let (X, Y ) be a random vector with joint density function of the form:f(X,Y )(x, y) = 24xy, 0 < x < 1, 0 < y < 1, x + y < 10 , otherwise(d) Check that E(E(X | Y )) = E(X).

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