Tri-State Pick 3 game: 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 Xis
Payoff X
SO
5500
The mean and standard deviation of X are wx = $0.50 and ox =
Probability: 0.999 0001
$15.80
Suppose you buy a 51 ticket on each of two different days
7. Find the expected payoff for the two tickets.
8. Find the standard deviation for the payout of the two tickets.
Suppose you buy a Pick 3 ticket every day for a year (365 days)
2. Find the mean of your total winnings.
10. Find the standard deviation of your total winnings

When booking personal travel by air, one is always interested in actually arriving at one’s final destination even if that arrival is a bit late. the key variables we can typically try to control are the number of flight connections we have to make in route, and the amount of layover time we allow in those airports whenever we must make a connection. the key variables we have less control over are whether any particular flight will arrive at its destination late and, if late, how many minutes late it will be. for this assignment, the following necessarily-simplified assumptions describe our system of interest: the number of connections in route is a random variable with a poisson distribution, with an expected value of 1. the number of minutes of layover time allowed for each connection is based on a random variable with a poisson distribution (expected value 2) such that the allowed layover time is 15*(x+1). the probability that any particular flight segment will arrive late is a binomial distribution, with the probability of being late of 50%. if a flight arrives late, the number of minutes it is late is based on a random variable with an exponential distribution (lamda = .45) such that the minutes late (always rounded up to 10-minute values) is 10*(x+1). what is the probability of arriving at one’s final destination without having missed a connection? use excel.