Exam MAS-I Practice Question 63

Study guide: Exam MAS-I

Claim sizes follow a gamma distribution with known shape \alpha = 3 and unknown scale \theta:

f(x) = \frac{x^{\alpha - 1} e^{-x/\theta}}{\Gamma(\alpha)\,\theta^{\alpha}}, \quad x > 0

A random sample of 25 claims will be used to estimate the mean claim size, \alpha\theta = 3\theta.

Calculate the Cramér–Rao lower bound for the variance of an unbiased estimator of the mean claim size, evaluated at \theta = 400. Give your answer as a whole number.

Answer this question and see the worked solution

Concepts tested

• Cramér-Rao Lower Bound
• Fisher Information
• Gamma
• Unbiasedness

More questions from this set

• Exam MAS-I Practice Question 62
• Exam MAS-I Practice Question 64