Let x be a random variable representing the amount won on a single lottery ticket. a) if the jackpot is worth $1,000,000, what is the expected value of x? b) what is your expected gain (gain = amount won – amount spent) when you buy one lottery ticket? c) what is the probability that you win $2 or more? d) at what jackpot amount would you expect to break even when you purchase a single lottery ticket? e) among players who win, what’s the expected amount won?