The following table shows the joint distribution of random variables X and Y.
Y=1 Y=2 Y=3 Y=4
X=1 0.04 0.03 0.02 0.01
X=2 0.08 0.06 0.04 0.02
X=3 0.12 0.09 0.06 0.03
X=4 0.16 0.12 0.08 0.04
Which of the following statements about the random variables X and Y is correct?
A: X and Y are independent because knowing the value of X does not change the probability distribution of Y.
B: X and Y are independent because knowing the value of X changes the probability distribution of Y.
C: X and Y are not independent because knowing the value of X does not change the probability distribution of Y.
D: X and Y are not independent because knowing the value of X changes the probability distribution of Y.
E: The independence of X and Y cannot be determined from the table.
