Examine the scatterplot matrix (generated by line 6) and answer the questions below. Include the scatterplot matrix with your answer.  (a) Components 2 and 3 are uncorrelated. Do they appear...

Examine the scatterplot matrix (generated by line 6) and answer the questions below. Include the scatterplot matrix with your answer.

 (a) Components 2 and 3 are uncorrelated. Do they appear independent? Why or why not?

 (b) Do you see signs of tail dependence? If so, where?

 (c) What are the effects of dependence upon the plots?

 (d) The nonzero correlations in the copula do not have the same values as the corresponding sample correlations. Do you think this is just due to random variation or is something else going on? If there is another cause besides random variation, what might that be? To help answer this question, you can get confidence intervals for the Pearson correlation: For example, 8 cor.test(rand_t_cop[,1],rand_t_cop[,3]) will give a confidence interval (95 percent by default) for the correlation (Pearson by default) between components 1 and 3. Does this confidence interval include 0.75?