SOLUTION: If the co-variance between two random variables X and Y is zero then A. X and Y are independent. B. Knowing the value of X provides no information about the value of Y . C. E(X)

Algebra ->  Probability-and-statistics -> SOLUTION: If the co-variance between two random variables X and Y is zero then A. X and Y are independent. B. Knowing the value of X provides no information about the value of Y . C. E(X)      Log On


   

Question 1042553: If the co-variance between two random variables X and Y is zero then
A. X and Y are independent.
B. Knowing the value of X provides no information about the value of Y .
C. E(X) = E(Y ) = 0.
D. None of the above.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
B. Knowing the value of X provides no information about the value of Y .
It cannot be A, since 0-covariance does NOT imply independence. (Although independence ===> 0-covariance.)
It cannot be C, because covariance could be zero but E(X) and E(Y) are NOT.
Now 0-covariance ===> 0-correlation ===> 0 coefficient of determination, which means the dependent variable cannot be predicted using the independent variable.