Q 6.2. Let X = (X1, X2, X3)T ~ MVN(µx, Ex) where -3 6 -2 -2 --() ----G70 and Σχ -2 2 1 -2 1 1 (a) Compute the moment generating function Mx(t) of X. (b) Compute E(X₁X₂). (c) Let Y₁ = 3X₂ X3+1 Y₂ = X1 - X2 - X3 Y3 = X₁ + 2X2 - 2. Compute the distribution of Y = (Y₁, Y2, Y3)T. -
Q 6.2. Let X = (X1, X2, X3)T ~ MVN(µx, Ex) where -3 6 -2 -2 --() ----G70 and Σχ -2 2 1 -2 1 1 (a) Compute the moment generating function Mx(t) of X. (b) Compute E(X₁X₂). (c) Let Y₁ = 3X₂ X3+1 Y₂ = X1 - X2 - X3 Y3 = X₁ + 2X2 - 2. Compute the distribution of Y = (Y₁, Y2, Y3)T. -
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.CR: Chapter 4 Review
Problem 5CR: Determine whether each of the following statements is true or false, and explain why. The chain rule...
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Q6.2
Transcribed Image Text:Q 6.2. Let X = (X1, X2, X3)T ~ MVN (ux, Ex) where
-3
Hx=
0
and
Ex =
(a) Compute the moment generating function Mx(t) of X.
(b) Compute E(X₁X₂).
(c) Let
6
-2
-2
-
Y₁ = 3X₂ X3+1
Y₂ = X₁ X2 X3
X1
Y3 = X₁ + 2X₂ - 2.
Compute the distribution of Y = (Y₁, Y2, Y3)¹.
-2 -2
2
1
1
1
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