6. [Use computer] Simulate 1,000 independent sets of i.i.d. standard Normal random numbers, with 40 observations in each set. Find the maximum absolute correlation coefficient among all pairs of sets of your simulated data. [Hint:] It is easier to generate a long vector of Normal random numbers: (e.g. x=rnorm(1000*40, 0, 1), then put it into a matrix with 1,000 columns (e.g. xx=matrix (x, ncol, nrow) ). You can subtract a diagonal matrix to remove the di- agonal from the correlation matrix (because the diagonal elements are always one), then use the absolute function and the max function on the resulting matrix to find the maximum absolute correlation coefficient in the matrix. Function cor(x) calculates the correlation among the columns. Function diag (1, ncol, nrow) creates a diagonal matrix. Function abs (y) gets the absolute value of y - elementwise when y is a matrix. . (a) Comment on the results. . (b) Without computation, what do you expect to see if there are 10,000 such independent sets (of 40 observations) and why? . (c) Without computation, what do you expect to see if there are 100 such inde- pendent sets (of 40 observations) and why