You and a friend play a game where you each toss a balanced coin. If the upper faces on the coins are both tails, you win $\$3 ;$ if the faces are both heads, you win $\$ 6 ;$ if the coins do not match (one shows a head, the other a tail), you lose $\$ 3$ (win $(-\$ 3)$ ). How much should you pay to play this game if your net winnings, the difference between the payoff and cost of playing, are to have mean O ? Calculate the mean and variance of $y$, your winnings on a single play of the game. Note that $E(Y)>0$. $E(Y)=\$ \square$ $V (Y)=\squares $1$$ SP.PC. 113