A$1 bet in a state lottery pick 3 game pays $500 if the 3-digit number you choose exactly matches the winning number, which is drawn at random. here's the distribution of the payoff x:

payoff x $0 $500
probability 0.999 0.001

each day's drawing is independent of other drawings.

a) what's the mean and the standard deviation of x?
b)joe buys a pick 3 ticket twice a week. what does the law of large numbers say about the average payoff joe receives from his bets?
c) what does the central limit theorem say about the distribution of joe's average payoff after 104 bets in a year?