Explain how to use the rejection method to simulate a random variable with the p.d.f. given by

f(x)=30(x^2-2x^3+x^4), 0

and f(x)=0 otherwise.This means, you should specify g and c, and state the method of simulation with the corresponding function g and value c. Is the choice of c unique? How should you select the value of c? 

Note:

Rejection method:
1. Simulate two independent random variables U and Y , where U follows U (0, 1) distribution, and Y has the p.d.f. g.
2 If U ≤ f(Y )/cg(Y), then stop and let X := Y ; otherwise, return to Step 1.

The random variable X produced in this way is with the p.d.f. f.