a$.$ Corporate triple A bond interest rates for $12$ consecutive months follow.

$9\mathrm{.}5,9\mathrm{.}3,9\mathrm{.}4,9\mathrm{.}6,9\mathrm{.}4,9\mathrm{.}3,9\mathrm{.}8,10\mathrm{.}5,9\mathrm{.}7,9\mathrm{.}7,9\mathrm{.}3,9\mathrm{.}8$

Develop three$-$month and four$-$month moving averages for this time series. Does the three$-$month or

four$-$month moving average provide the better forecasts based on MSE? Explain. What is the moving

average forecast for the next month?

b$.$ Consider a binomial experiment with $2$ trails and p $=0\mathrm{.}53.$

i$.$ Compute f$(2).$

ii$.$ Find the probability of at least one success.

iii. Find the expected value, variance, and standard deviation.