TMA4267 Linear Statistical Models Part 1: Multivariate random variables and the multivariate normal distribution by Mette Langaas https://padlet.com/mette_langaas/kvaua8nuc1rx What are the important results in this part of the course? en-us 2017-01-26 20:13:59 UTC 2026-02-26 13:03:47 UTC hello@padlet.com https://padlet-assets.s3.amazonaws.com/icons/Thunder.png X is a p-dimensional vector of random variables with mean (p-dimensional vector) mette_langaas https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149749975 \mu=\text{E}(X)
and covariance matrix (p times p symmetric and positive definite matrix) 
\Sigma=\text{Cov}(X)=

\text{E}((X-\mu)(X-\mu)^T)=

\text{E}(XX^T)-\mu \mu^T.]]> 2017-01-26 20:14:13 UTC https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149749975 X is a p-dimensional random vector and C is k times p constant matrix. mette_langaas https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149785649 \text{E}(CX)=C \text{E}(X)

\text{Cov}(CX)=C \text{Cov}(X)C^T]]> 2017-01-27 00:05:43 UTC https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149785649 V and W are random vectors. The covariance between V and W is mette_langaas https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149785834 \text{Cov}(V,W)=

\text{E}((V-\text{E}(V))(W-\text{E}(W))^T)

= \text{E}(VW^T)-\text{E}(V)\text{E}(W^T)]]> 2017-01-27 00:09:01 UTC https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149785834 Multivariate momentgenerating function (MGF) for p-dimensional X: mette_langaas https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149804316 M_X(t)=\text{E}(exp(t^TX))
where t is p-dimensional vector.
]]> 2017-01-27 06:53:37 UTC https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149804316 Mean of quadratic form "the trace formula" mette_langaas https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149804428 \text{E}(X^TAX)=tr(A\Sigma)+\mu^T A \mu
where X is a p-dimensional random variable with mean and covariance 
\text{E}(X)=\mu, \text{Cov}(X)=\Sigma
and A is a p times p constant matrix.

]]> 2017-01-27 06:56:17 UTC https://padlet.com/mette_langaas/kvaua8nuc1rx/wish/149804428