4. A certain lottery sells 3 million tickets for $2 each. Let X denote your winnings upon purchasing 1 ticket, and suppose * has the following probability distribution P(* = =) $1. DO0, 000 $100, DOO 10 $5. 000 3,000 000 $0 2.999 809 3,000 000 a] What is the expected value of X. (2 marks] b) Since each ticket costs $2, define Y=X-2 to be your profit from purchasing 1 ticket Compute and interpret the expected value of Y. [2 marks] c) Suppose you purchase 100 tickets. What is the probability that you win any amount of money among all 100 tickets? For simplicity, assume independence. (3 marks]