I can't make out a couple of things about the Bernoulli distribution. Help would be greatly appreciated.
200 lottery tickets cost USD 1 each. One of them gives a win of USD 101 (the cost plus 100). The remaining ones give no return (loses a dollar). Let Z denote the net result when purchasing one lottery ticket. Find the probability function for Z and calculate the expected value and the variance.
Clearly, $p_z(-1)=0.995$, and $p_z(101)=0.005$. One of these should represent $p$ in the Bernoulli distribution according to the definition, surely?
Now, the expected value $E(Z)$ is supposed to equal $p$, but it turns out that $E(Z)=-0.495$. How does that happen?