If X, Y and Z are uncorrelated statistical variables with standard deviations 5,12 and 9
U= X+Y , V = Y+Z. then the correlation coefficient between U and V is ;
12/65
144/288
48/65
144/169
Cov[U,V] = Cov[X+Y, Y+Z] = Cov [X,Y] + Cov [X,Z] + Cov [Y,Y] +Cov[Y,Z]
Now since X,Y,Z are independent, their respective covariances with each other will be 0.
That leaves us with Cov[X+Y,Y+Z] = VarY = 122
Similarly, take out Var(U) and Var(V) and use the correlation coefficient formula.
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