Question 1155648
Pay a dollar, and roll a die.
If you guess the number correctly, you get $6, otherwise you lose your $1.
E(X)=$6*(1/6)-$1(6/6). Note: You don't get your dollar back at all, so there is at least a $1 loss. But in 1/6 chances you get $6, which will make the E(X)=0