1. Two fair coins are flipped and random variables X and Y are defined according to the outcomes as follows.
x= 1 if the first coin lands heads up, 0 if it lands tails
y= 1 if the second coin lands heads up, 0 if it lands tails
- Calculate E(X), E(Y), Var(X), Var(Y), and Cov(X,Y).
- Describe the probability distribution of Z = X - Y.
- Calculate E(Z), Var(Z), and Cov(Z, X).