Answer:
Cov(X, Y) = 0
Step-by-step explanation:
X = Sum of the outcomes
Y = Difference between the outcomes (first - second)
Let the two outcomes of the die be A and B
X = A + B
Y = A - B
Cov(X, Y) = Cov( A+B, A-B)
Cov(X, Y) = Cov(A,A) - Cov(A,B) + Cov(B,A) - Cov(B,B)
Cov(X,Y) = Cov(A, A) - Cov(B, B)
Cov(X, Y) = Var(A) - Var(B)
A and B are identically distributed, Var(A) = Var(B)
This means that: Cov(X, Y) = 0
