What is covariance and correlation between two random variables regarding coin flips?
So say Coin A has probability 1/3 of heads and Coin B has probability 2/3 of heads. You pick one of the two coins at random (50% chance of A or B) then flip that coin twice. If X is 0 if tails on first flip, 1 if heads on first flip, and Y is 0 if tails on second flip, 1 if heads on second flip, what would the covariance and correlation be for X and Y?
Looking for cov(X,Y) and cor(X,Y). I keep getting confused on how to set it up, and my numbers don't make sense.