Homework Problem 9, Due Friday February 22.
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The objective in this problem is to simulate data 
from an unfamiliar but not too exotic univariate 
density, by two different methods, and compare the 
results.

(a) Write a function to generate  N  random variates 
X_1, ..., X_N  for the density

f(x)  =  c log(1+x) x^2 e^{-x} , x > 0

where c = 0.3851565  is determined by the condition 
that f(x) integrates to 1 on (0,infty). In this part, 
use a method directly based on the probability integral 
transform, using a parallelizable evaluation (or highly 
accurate approximation)  of the inverse distribution 
function F^(-1).

(b) Write a function to do the same task as in part (a),
using an Accept/Reject Method.

(c) Test the two functions you have written, possibly 
against each other, using a formal chi-square goodness 
of fit test. Also test which method works faster. (The 
answer to this may well depend on how accurately you 
have chosen to approximate the df in (a).)