Answered: Q 6.2. Let X = (X1, X2, X3)T MVN(x, Ex)… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.4: Values Of The Trigonometric Functions

Problem 23E

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Q 6.2. Let X = (X₁, X2, X3)T~ MVN(ux, Ex) where
-3
*-()
=
1
and Ex=
=
(a) Compute the moment generating function Mx(t) of X.
(b) Compute E(X₁ X₂).
(c) Let
Y₁
Y2
Y3 =
Compute the distribution of Y = (Y₁, Y2, Y3)T.
6
-2 -2
-2 2 1
-2
1
1
= 3X2 X3 + 1
X₁ X₂ X3
X₁ + 2X₂ - 2.
=
-

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Q 6.2. Let X = (X1, X2, X3)T ~ MVN(µx, Ex) where -() fx = and Ex = Y₁ Y₂ Y3 Compute the distribution of Y = (Y1, Y2, Y3)T. = = ( (a) Compute the moment generating function Mx (t) of X. (b) Compute E(X₁X₂). (c) Let = 6 -2 -2 -2 -2 2 1 1 1 3X2 X3 + 1 X₁ X₂ X3 X₁ + 2X2 - 2.
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Q 6.2. Let X = (X1, X2, X3)¹ ~ MVN(µx, Ex) where -3 -(1) μx = and Σχ = (a) Compute the moment generating function Mx (t) of X. (b) Compute E(X₁X2). (c) Let Y₁ Y₂ Y3 Compute the distribution of Y= (Y₁, Y2, Y3)T. = = 6 -2 -2 = -2 2 1 3X2 X3 +1 X₁ - X₂ - X3 X₁ + 2X₂ - 2. -2 1 1
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