6. In a statewide lottery, one can buy a ticket for $1. With probability .0000001. one wins a million dollars (S1,000,000). and with probability .9999999 one wins nothing (SO).

a) Let Y denote the winnings from buying one ticket. Construct the probability distribu- tion for Y. Show that the mean of the distribution equals 10. corresponding to an expected return of 10 cents for the dollar paid.

b) The profit X from buying a single $1 ticket equals the winnings from playing the lottery minus the dollar paid for the ticket. that is. X Y 1. Construct the probability distribution of X. and find its mean. Interpret