4. (2) The Mississippi Lottery website [Powerball - Mississippi Lottery (mslotteryhome.com)] gives the following payout odds when you purchase a $2 Powerball ticket, based on a grand prize of $20 million. {Note: the grand prize odds decrease as the jackpot grows since more people purchase tickets.} Probability 0.000000003422 0.000000085557 0.000001095136 0.000096372574 0.003150671455 0.037185354691 0.959566417165 Payout $20 million $1 million $50,000 $100 $7 $4 $0 a) Compute the expected value, E(X). b) Compute the variance, Var(X). Hint: See equation (P.13). c) If you purchased 40 tickets (for $80) as a Christmas present for a friend, what was the expected value of your gift?