CAS Exam MAS-I Spring 2019, 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 a beta distribution, f(x), with parameters a = 2, b = 10, \theta = 1, and is concentrated on the interval (0, 1).
• The rejection method uses 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 U \leq \dfrac{f(Y)}{c\,g(Y)} stop and set X = Y. Otherwise return to Step 1.

Calculate the minimum possible value for c.

• A) Less than 3.0
• B) At least 3.0, but less than 3.5
• C) At least 3.5, but less than 4.0
• D) At least 4.0, but less than 4.5
• E) At least 4.5

Answer this question and see the worked solution

Concepts tested

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

More questions from this set

• CAS Exam MAS-I Spring 2019, Question 13
• CAS Exam MAS-I Spring 2019, Question 15