In a bivariate distribution $$X_i, y_i, i = 1, 2, ....., 8$$, if $$d_i$$ is the deviation between the the ranks of $$X_i$$ and $$Y_i$$ and and $$\sum_{i = 1}^{8} d_i^{2} = 21$$ then the coeffefficient of rank correlation between $$X_i$$ and $$Y_i$$ is

 If X1, X2, ... , Xn are mutually independent normal random variables with means μ1, μ2, ... , μn and variances σ21,σ22,⋯,σ2nσ12,σ22,⋯,σn2, then the linear combination 

of ranks  $$X_i$$ and $$Y_i$$ means have equal value 4 and 4 as i = 1,2,3,4......8 

    Y =  $$\sum_{i = 1}^{8} d_i^{2} $$ = 21 

Then, finding the probability that X is greater than Y reduces to a normal probability calculation:

P(X>Y )= P(X − Y > 0) = P( Z > 0 − 1\4 ) = P(Z>−0.75 ) = P(Z<0.75) = 0.75 Answer