Q1) $1.00 bet is state lottery's pick 3 game pays $500 if three-digit number you select exactly matches winning number, which is drawn at random.  Here is distribution of payoff X:

Each day's drawing is independent of other drawings:

a) Compute the mean and standard deviation of X?

b) John purchases a Pick 3 ticket every day.  What does law of large numbers say about average payoff John receives from his bets?

c) What does central limit theorem say about distribution of John's average payoff after 365 bets in a year?

d) John comes out ahead for year if his average payoff is greater than $1.00 (amount he spends each day on a ticket). Find outs the probability that John ends the year ahead?