A lottery that sells 150,000 tickets has the following prize structure:

(1) first prize of $1000

(2) 5 second prizes of $200

(3) 25 third prizes of $100

(4) 1000 fourth prizes of $20

(a) Let be the winning amount of a randomly drawn lottery ticket.List the probability distribution of for each of the prizes.Table of and (x).

(b) Compute the mean or expected payout value of the ticket.

(c) Compute the variance of this distribution.(2 Points) Comment on the usefulness of the variance as a measure of dispersion for this distribution