Let S1 = X1 + Y1, S2 = X2 + Y2, .., S40 = X40 + Y40 be a sample where

X1, X2, .., X40 is a sample from Unif(-1,1), and

Y1, Y2, .., Y40 is a sample from Exp(1.1).

Calculate the upper-tailed, two-tailed, and lower-tailed 90% confidence interval for the variance of S.

Note: Use at least a hundred thousand simulated samples to generate sampling distribution for the variance of S.

Hint: Variance must be computed as the sample variance of the sequence of 40 numbers s1,s2,...,s40, where s1 is the sum of the first random number from the Unif(-1,1) and the first random number from the Exp(0.65), etc. Think of sequence (vector) s as the entry-by-entry sum of sequences (vectors) x and y.