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

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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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. = -
Transcribed Image Text: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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