In a weekly lottery, each $1 ticket sold adds 50 cents to the jackpot that starts at $1 million before any tickets are sold. The jackpot is announced each morning to encourage people to play. On the morning of the ith day before the drawing, the current value of the jackpot J: is announced.
On that day, the number of tickets sold. Ni is a Poisson random variable with expected value J. Thus, six (lays before the drawing. the morning jackpot starts at $1 million and N6 tickets are sold that day. On the day of the drawing, the announced jackpot is Jo dollars and N0 tickets are sold before the evening drawing. What are the expected value and variance of J, the value of the jackpot the instant before the drawing?