Question: The Tri-State Pick 3 Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont. You choose a number with 3 digits from 0 to 9; the state chooses a three-digit winning number at random and pays you $500 if your number is chosen. Because there are 1000 numbers with three digits, you have probability 1/1000 of winning. Taking X to be the amount your ticket pays you, the probability distribution of X is
(a) Show that the mean and standard deviation of X are μX = $0.50 and σX = $15.80.
(b) If you buy a Pick 3 ticket, your winnings are W = X - 1, because it costs $1 to play. Find the mean and standard deviation of W. Interpret each of these values in context.