Question

P \begin{pmatrix} \begin{bmatrix} X \\ Y \\ Z \end{bmatrix} \end{pmatrix} = N \begin{pmatrix} \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \begin{bmatrix} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix} \end{pmatrix}.

          P \begin{pmatrix} \begin{bmatrix} X \\ Y \\ Z \end{bmatrix} \end{pmatrix} = N \begin{pmatrix} \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \begin{bmatrix} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix} \end{pmatrix}.

P
< p m a t r i x >
= N
< p m a t r i x >
.

Added by Michelle H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/09/2023

Step 1

Step 1: To determine the distribution of U=x+Y+Z, we need to find the mean and variance of U. Show more…

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Regarding mathematical statistics: Assume that the vector x=(x,Y,Z)inR^(2) has a trivariate normal distribution whereP([[x],[Y],[Z]])=N([[0],[0],[0]],[[2,1,0],[1,2,0],[0,0,4]]) Let U=x+Y+Z. (a) Determine the distribution of U=x+Y+Z. (b) Determine the conditional expected value E(e^(2x)|U). [0] [2 1 01 0 1 2 0 0 0 0 4 x P = N Z