CAS Exam MAS-I Spring 2018, Question 14

Study guide: Exam MAS-I

You are given the following simulation process to generate random variable X using the rejection method:

• X has density function: f(x) = 12x(1-x)^2, for 0 < x < 1
• The rejection method is based on g(x) = 1, for 0 < x < 1
• The rejection procedure is as follows:
  • Step 1: Generate independent random numbers Y and U, which are both uniform on (0,1).
  • Step 2: If rejection function, h(Y), is true, stop and set X = Y. Otherwise return to Step 1.

Determine which of the following is a form of the rejection function h(Y).

• A) U \le \frac{27}{4} Y(1-Y)^2
• B) U \ge \frac{27}{4} Y(1-Y)
• C) U \le 16\, Y^2(1-Y)^2
• D) U \ge \frac{27}{4} Y^2(1-Y)^2
• E) The answer is not given by (A), (B), (C), or (D)

Answer this question and see the worked solution

Concepts tested

• Rejection Method
• Uniform Continuous Distribution
• Probability Density Function (PDF)

More questions from this set

• CAS Exam MAS-I Spring 2018, Question 13
• CAS Exam MAS-I Spring 2018, Question 15