This problem is based on the data contained in the data set UTILITIES included in the library Rsafd. It is a matrix with two columns, each row corresponding to a given day.

The first column gives the log of the weekly return on an index based on Southern Electric stock daily close and capitalization, (we’ll call that variable X), and the second column gives, on the same day, the same quantity for Duke Energy (we’ll call that variable Y ), another large utility company.

1. Compute the means and the standard deviations of X and Y , and compute their correlation coefficients.

2. We first assume that X and Y are samples from a jointly Gaussian distribution whose parameters are equal to the estimates computed in question 1. Using the assumption of joint normality, compute the 2-percentiles of the variables X + Y and X − Y , and compute the empirical estimates of these percentiles