Each day, Amy eats lunch at the cafeteria. She chooses pizza as her main dish with probability 40%, and her behavior each day is independent of all the other days. Let X denotes the number of days she chooses pizza in a 10-day period. Let Y = 10 - X denote the number of days in which Amy does not eat pizza.
a. Are X and Y dependent or independent?
b. Find the covariance Cov (X, Y) of X and Y.
c. Find the correlation p(X, Y) of X and Y.