If X and Y are any random variables with COV(X,Y)= 0.25, ,then the coefficient of correlation ρ is
A)1.417
B)1.190
C)0.595
D)0.354

Question

If X and Y are any random variables with COV(X,Y)= 0.25,  ,then the coefficient of correlation ρ is
A)1.417 
B)1.190 
C)0.595 
D)0.354

Quizplus · Accepted Answer

The coefficient of correlation is defined as ρ = COV(X,Y)/σ_X σ_Y, where σ_X and σ_Y are the standard deviations of X and Y respectively.
Since COV(X,Y) = 0.25 and we don't know the values of the variances, we cannot directly calculate ρ. However, we know that -1 ≤ ρ ≤ 1, because ρ is a correlation coefficient and must lie within this range.
Option A and B are greater than 1, which is not possible for a correlation coefficient. Therefore, we can eliminate them.
Option D is less than 0.25, which means that the standard deviations σ_X and σ_Y would have to be greater than the expected values of X and Y, which is unlikely. Therefore, we can eliminate this option as well.
Option C is the only remaining option and lies within the possible range of correlation coefficients. Therefore, we choose option C as the answer.

If X and Y Are Any Random Variables with COV(X,Y)=