Given below are the monthly values of the S$\backslash$&P $500$ Index. Suppose that in each month you had written an out$-$of$-$the$-$money put option on one unit of the index with an exercise price $\backslash (5\backslash \%\backslash )$ lower than the current value of the index.equired: $1.$ What would have been the average value of your gross monthly payouts on the puts over the $10-$year period October $1977$ September $1987?($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$ Answer is complete but not entirely correct. a$-2.$ The standard devlation? $($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$ b$-1.$ What would have been the average value of your gross monthly payouts on the puts if you extend the sample by one month to include October $1987?($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$b$-2.$ The standard deviatipn? $($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$