1. Consider a model where the annual return on the S&P500 is positive 70% of the time and negative 30% of the time and whether the S&P500 goes up or down is independent from one year to the next. Hence if X is the number of times that the market goes up in the next 10 years then X is a Binomial (10, 0.7). a. A contract pays off $10 for each year that the S&P500 return is positive in each of the next 10 years. The payoff is then given by P=$10*X. What is the expected payoff on this contract? b. What's the variance of the payoff? c. What is the probability that 6 out of 10 years the annual return on the S&P500 is positive