Question

If the covariance matrix of a 3x1 random vector X is Kx = ? 1 0 1 ? ? 0 2 2 ? ? 1 2 4 ? Find the correlation coefficient between X1 and X2. Find the correlation coefficient between X1 and X3. Find Var(X1 + X2 + X3) Note: They are not necessarily independent.

          If the covariance matrix of a 3x1 random vector X is

Kx = ? 1 0 1 ?
     ? 0 2 2 ?
     ? 1 2 4 ?

Find the correlation coefficient between X1 and X2.
Find the correlation coefficient between X1 and X3.
Find
Var(X1 + X2 + X3)

Note: They are not necessarily independent.

If the covariance matrix of a 3x1 random vector X is

Kx = ? 1 0 1 ?
? 0 2 2 ?
? 1 2 4 ?

Find the correlation coefficient between X1 and X2.
Find the correlation coefficient between X1 and X3.
Find
Var(X1 + X2 + X3)

Note: They are not necessarily independent.

Added by Nathan H.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

08/19/2023

Step 1

The correlation coefficient between two random variables Xi and Xj is given by: ρ(Xi, Xj) = \frac{Cov(Xi, Xj)}{\sqrt{Var(Xi) \cdot Var(Xj)}} For X1 and X2: ρ(X1, X2) = \frac{Cov(X1, X2)}{\sqrt{Var(X1) \cdot Var(X2)}} = \frac{0}{\sqrt{1 \cdot 2}} = Show more…

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If the covariance matrix of a 3x1 random vector X is Kx = (1 0 1 0 2 2 1 2 4) Find the correlation coefficient between X1 and X2. Find the correlation coefficient between X1 and X3. Find Var(X1 + X2 + X3) Note: They are not necessarily independent.