2. In a lottery style game. 5 balls will be randomly selected, without replacement, from an um containing 45 balls numbered 1 through 43. To play this lotto once, you pay $1 and you will pick 5 numbers. Five correct numbers wins you $10,000, 4 correct numbers wins you $5000, 3 correct numbers wins you $500. 2 correct numbers wins you $10, 1 conect number wins you $1, and for no correct numbers you win $0 (in other words, you will lose $1). Let Y denote the total "profit" made when playing this lotto. [Hine You paid a dollar, so your profit is 1 dollar less than the amount you win ] (a) (6 pts) Find the probability distribution for Y. You can leave your probabilities as fractions for this problem. (b) (3 pts) Find the expected value E()) and the variance V(Y) of the profit, when playing this lotto.(Round your answers to the nearest cont.)