4. A certain lottery sells 3 million tickets for $2 each. Let X denote your winnings upon purchasing 1 ticket, and suppose X has the following probability distribution P(X = x) $1, 000, 000 1 3.000,060 $100, 000 10 3,000,009 $5,000 3,000 060 2999 464 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]