At a certain retailer, purchases of lottery tickets in the nal 10 minutes of sale before a draw follow a Poisson distribution with = 15 if the top prize is less than $10,000,000 and follow a Poisson distribution with = 10 if the top prize is at least $10,000,000. Lottery records indicate that the top prize is $10,000,000 or more in 30% of draws.
a) Let Y be the number of tickets sold in the nal 10 minutes before a lottery draw. Give the probability mass function for Y .
b) Find the mean and variance of Y .
c) If fewer than 10 tickets are sold in the nal 10 minutes of sale before a particular draw, what is the probability that the top prize in that draw is $10,000,000 or more?