Probability covariance correlation coefficient

D(Z) can't be counted like this, only independence can be counted like this.

D(Z)=D(X/2-Y/3)-Cov(X/2-Y/3，X/2-Y/3)

=Cov(X/2，X/2)+Cov(Y/3Y/3)-2Cov(X/2，Y/3)

=D(X)/4+D(Y)/9-2/6*Cox(X，Y)

= 16/4+9/9-2/6 *6

=3

Next, calculate CoV (x, z) = CoV (x, x/2-y/3) = CoV (x, x/2)-CoV (x, y/3).

=D(X)/2-Cov(X，Y)/3= 16/2-6/3=6

So ρ = CoV (x, z)/(d (x) d (z))1/2 = 6/(16 * 3)1/2 = 3/2 radical (3).

The things in the cover can be divided. Keep this in mind, and it will be much easier to do the problem in the future.