Homework Problem 12, Due Friday February 27.
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(a) Generate 1000 independent random 3-vectors 
(X,Y,Z) which are uniformly distributed on the region:

X, Y, Z >= 0, X+Y <=1, X+Z<=1, Y+Z <= 1.5.

Do this by two completely different methods, yielding
distinct and independent 1000 x 3 matrices M1 and M2, each 
with independent rows.

(b) Use a chi-square goodness of fit test to test 
whether the two sets of points you generated in 3 dimensions, 
as the rows of M1 and M2, have the same distribution.

(c) Use (two-sample) Kolmogorov-Smirnoff tests to check 
that the elements of column j of M1 have the same distribution 
as the elements of column j of M2, for j=1,2,3.