Homework Problem 6, Due Monday September 28.
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In EACH of the following two situations, write TWO 
separate functions, to simulate N independent random 
2-vectors of the described distribution BY TWO COMPLETELY 
DIFFERENT METHODS. You might use methods related 
to repeated univariate probability integral transforms, 
to accept-reject methods, or to a simple mapping of 
an easier-to-generate random 2-vector.

(a) Simulate a random two-dimensional vector variable  
(X,Y)  with joint density

f(x,y)  =  (1.5/x^2) * (1/max(x^2, y^2)) ,  for    x, y > 1,  


(b) Generate independent random points points (X_i,Y_i) 
uniformly distributed within the triangle which has one 
side equal to the segment from (0,0) to (6,0) on the  
x-axis and which has opposite vertex (-3,4). 


In both parts (a) and (b), you should test the output of 
your functions for appropriate behavior, in terms of histograms 
versus (marginal) densities, of various theoretical versus 
simulated probabilities, and/or theoretical versus 
empirical marginal distribution functions. In particular, 
your test in (b) should confirm [persuasively, if not 
exhaustively] that the points you generate are uniformly 
distributed in the triangle.