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1. Assume a random vector X =X1X2X3X4 follows a multivariate normal distribution with the following mean vector and covariance matrix. Let X) - [X1X2 and X2) = [X3X4) be the partition of X. Define 3 -1 2 -1 4 2 1 5 HX = Ex -1 Find (Note you don't need to carry out the final answers. You only need to set up the forms with related numerical values in place.) (a) E(X- X2+ X3- X4) (b) Var(X1 - X2 + X3 - X4) (e) COV(x), x2) (d) COV (3X + X Xx)

1. Assume a random vector X =X1X2X3X4 follows a multivariate normal distribution with the following mean vector and covariance matrix. Let X) - [X1X2 and X2) = [X3X4) be the partition of X. Define 3 -1 2 -1 4 2 1 5 HX = Ex -1 Find (Note you don't need to carry out the final answers. You only need to set up the forms with related numerical values in place.) (a) E(X- X2+ X3- X4) (b) Var(X1 - X2 + X3 - X4) (e) COV(x), x2) (d) COV (3X + X Xx)

Calculus For The Life Sciences
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.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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1. Assume a random vector X = X,X2X3X4 follows a multivariate normal distribution with the following mean vector and covariance matrix. Let X) = [X1X2 and X(2) = [X3X4 be the partition of X. Define -- -) 3 -1 2 -1 4 Ex 2 1. Find (Note you don't need to carry out the final answers. You only need to set up the forms with related numerical values in place.) (a) E(X1-X2+ X3- X4) (b) Var(X1 - X2 + X3 - X4) (c) COV(X), x(2) (d) COV (3X1 + X2, X3) (e) Set up the conditional expectation and variance of X(2) and specify the distribution.
Transcribed Image Text:1. Assume a random vector X = X,X2X3X4 follows a multivariate normal distribution with the following mean vector and covariance matrix. Let X) = [X1X2 and X(2) = [X3X4 be the partition of X. Define -- -) 3 -1 2 -1 4 Ex 2 1. Find (Note you don't need to carry out the final answers. You only need to set up the forms with related numerical values in place.) (a) E(X1-X2+ X3- X4) (b) Var(X1 - X2 + X3 - X4) (c) COV(X), x(2) (d) COV (3X1 + X2, X3) (e) Set up the conditional expectation and variance of X(2) and specify the distribution.
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