Dse 2005 doubt

[Ansh malhotra]

[Ansh malhotra]

What is the intuition behind such questions please help

[knowpraveen]

r^2= [cov(U,V)]^2/var(U)var(V)

cov(U,V)=0+var(Y)+0 since co-efficients of X and Y are zero.

And, var(U)=var(X)+var(Y) since X and Y are uncorrelated (so, Rxy=0)
Same for var(V).

Therefore, r^2 = (var Y)^2/(varX+varY)(varY+varZ)

= 144*144/(165)(225)

Therefore, r=48/65