Homework Problem Set 7, Due Wednesday October 4, 2017.
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Assigned       9/25/2017,  due 10/4:       12 points

Write a function to generate [as quickly and efficiently as possible] 
each of the following two types of random variables or vectors. 
IN BOTH PARTS, GENERATE THE RANDOM VARIABLES WITH EXACTLY CORRECT 
DENSITY, BY AN ACCEPT-REJECT METHOD.
Generate 1000 iid copies of each type of variable or vector, and present 
some kinds of test or graphical confirmation that your variables have 
the right density or distribution function.

(a) A random vector (X_i,Y_i) with joint density f(x,y) on the positive 
quadrant equal to   K xy/(1+x^2+y^2)^5   for x,y>0  and equal to 0 for 
other x,y.  Here  K  is a constant > 0 for you to determine.

[HINT: you may find that the random variables are easier to generate 
after transforming them to polar coordinates and then transforming them 
back to x,y coordinates.]

(b) A random variable X_i with density f(x) = C*(1+abs(x))*exp(-x^2) 
for  -1 < x < 1  and equal to 0 elsewhere, where  C  is a constant for 
you to determine.

NEXT HOMEWORK WILL BE POSTED BY FRIDAY AND WILL BE DUE MONDAY 10/9.