You’ve been given a lottery ticket with five mutually exclusive outcomes. you could, with probability 1/20,000, win a grand prize valued at $8,000. you could also, with probability 1/20,000, win a major prize valued at $4,000. a minor prize valued at $150 can be won with probability 1/5,000; and a very minor prize of value of $3 can be won with probability 1/150. finally, you could win nothing (valued at $0). find the mean and standard deviation of the value of your lottery ticket.