.
Using R, simulate n pairs of observations (Xi, Yi), i = 1, 2, . . . , n
from the distribution in the t
(a) From these observations calculate the estimates X￣, Y￣ , s2
X, and s2
Y (see
(2.18), (2.19)).
(b) Calculate the estimate s2
X,Y of Cov(X, Y ) defined by
s2
(c) Calculate the estimate r of the correlation coefficient ρ via r = s2
X,Y /(sX sY ).
(d) Compare the estimated covariance and correlation obtained for different
values of n with the theoretical values obtained in Exercise 12.