CAS Exam MAS-I Fall 2018, Question 15

Study guide: Exam MAS-I

You are given the following:

• A random variable, X, is uniformly distributed on the interval (0, \theta)
• \theta is unknown
• For a random sample of size n an estimate of \theta is given by:

\hat\theta = \frac{2}{n}\sum_{i=1}^{n} X_i

Calculate \operatorname{Var}(\hat\theta).

• A) \dfrac{4\theta^2}{3n}
• B) \dfrac{\theta^2}{3n^2}
• C) \dfrac{\theta^2}{12}
• D) \dfrac{\theta^2}{6}
• E) \dfrac{\theta^2}{3n}

Answer this question and see the worked solution

Concepts tested

• Statistics
• Uniform Continuous Distribution
• Variance
• Sample Mean

More questions from this set

• CAS Exam MAS-I Fall 2018, Question 14
• CAS Exam MAS-I Fall 2018, Question 16