The probability distribution of X = [X1, X2, ..., X,]' is given by the joint PDF f (x) = (27)¯P/2 e-a'e -p/2 1+||x;e- , x E RP. i=1 Show that any proper subset of X1, X2, ... , X, consists of mutually independent random variables which have a joint distribution that is multivariate normal, but X itself is not multivariate normal and the components of X are not independent.
The probability distribution of X = [X1, X2, ..., X,]' is given by the joint PDF f (x) = (27)¯P/2 e-a'e -p/2 1+||x;e- , x E RP. i=1 Show that any proper subset of X1, X2, ... , X, consists of mutually independent random variables which have a joint distribution that is multivariate normal, but X itself is not multivariate normal and the components of X are not independent.
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.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 6CR
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![The probability distribution of X = [X1, X2, . ..,Xp]' is given by the joint PDF
f (x) = (27)¯P/² e
+
X¿e
x E RP.
i=1
Show that any proper subset of X1, X2, ..., X, consists of mutually independent random variables
which have a joint distribution that is multivariate normal, but X itself is not multivariate normal
and the components of X are not independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbca55d5a-4c0c-453b-b624-8aa6a89b3c63%2F88861648-53a9-4384-b5db-1d61e0761aeb%2Fitao9wj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The probability distribution of X = [X1, X2, . ..,Xp]' is given by the joint PDF
f (x) = (27)¯P/² e
+
X¿e
x E RP.
i=1
Show that any proper subset of X1, X2, ..., X, consists of mutually independent random variables
which have a joint distribution that is multivariate normal, but X itself is not multivariate normal
and the components of X are not independent.
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