4. A certain lottery sells 3 million tickets for $1 each. Let X denote your winnings upon purchasing 1 ticket, and suppose X has the following probability distribution X P(X = x) $1,000,000 1 = 0.00000033 3,000,000 $100,000 10 = 0.00003 3,000,000 $5,000 100 0.000033 3,000,000 $0 2,999,889 0.999963 3,000,000 a) What is the expected value of X. (2 marks) H = EXp(X=x)= 1 000 000(0.00000033) + 100 000(0.0000033) + 5 000(0.000033) + 0 (0.999963) = 0.82965