7) Given a probability distribution F and a point x 6 Rd, at depth Mam“ D measures . ‘ _ dhow close x is to the center of the distribution and defines a rank order on pomt-S m R with respect to F. Observations which are far from the center of the data are given low ranks, whereas observations close to the center receive higher ranks. The Mahalano‘oisdepth MD“; F) of a vector is with respect to a distribution function F with mean vectorpiF and dispersion matrix 2;: is defined to be MD(t; F) = [1 + it — #F)’231(t — “tell—1- The sample version is computed by plugging in estimated ftp and $1.1. 0 5.. Write a program to generate a sample of size n from a bivariate normal distribution(F) with mean up = (O, 0), unit variances and Correlation 0.5. If you code in R1 see the function mahalanobis(x, center, cov). Let n = 10. Print the observations, theirmean and covariance, and the depth of each data point. Find and print the bivariate median; i.e. the bivariate vector that maximizes the depth function. e b. Generate n = 1000 bivariate observations from F. Plot all observations and identify the lowest 5 percent of the data in red.

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