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

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)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
Transcribed Image Text: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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