A $1.00 bet is a state lottery's pick 3 game pays $500 if the threedigit number you select exactly matches the winning number, which is drawn at random. Here is distribution of payoff X:
PayoffX

$0.00

$500.00

Probability

0.9999

0.001

Each day's drawing is independent of other drawings:
a) What are the mean and standard deviation of the X?
b) Joe buys a choose 3 ticket every day. What does the law of large numbers say regarding the average payoff Joe receives from his bets?
c) What does the central limit theorem say regarding the distribution of Joe's average payoff after 365 bets in the year?
d) Joe comes out ahead for the year if his average payoff is bigger than $1.00 (the amount he spends each day on a ticket). Find out the probability that Joe ends the year ahead?