CAS Exam MAS-I Fall 2019, Question 22

Study guide: Exam MAS-I

You are given the following information about a sample, X_1 \ldots X_n:

• X_i's are all mutually independent
• X_i \sim \text{Gamma}(\alpha_i, \theta), for i = 1, 2, \ldots n
• \alpha_i = \frac{1}{n} for all i
• Y = \sum_{i=1}^{n} X_i

Calculate the probability that Y > \theta.

• A) Less than 0.2
• B) At least 0.2, but less than 0.4
• C) At least 0.4, but less than 0.6
• D) At least 0.6, but less than 0.8
• E) At least 0.8

Answer this question and see the worked solution

Concepts tested

• Gamma
• Exponential Distribution
• Linear Combinations of Random Variables

More questions from this set

• CAS Exam MAS-I Fall 2019, Question 21
• CAS Exam MAS-I Fall 2019, Question 23