Exam MAS-I Practice Question 62

Study guide: Exam MAS-I

Annual claim counts on four independent policies follow a Poisson distribution with unknown mean \lambda. The observed counts are:

x_1 = 1, \quad x_2 = 0, \quad x_3 = 2, \quad x_4 = 1

The quantity of interest is P(N = 1) = \lambda e^{-\lambda}, the probability that a policy has exactly one claim. An analyst starts from the unbiased estimator W = \mathbf{1}\{X_1 = 1\} and improves it by conditioning on Y = X_1 + X_2 + X_3 + X_4.

Calculate the resulting estimate E[W \mid Y] for these data.

• A) 0.3164
• B) 0.3679
• C) 0.4219
• D) 0.5000
• E) 1.0000

Answer this question and see the worked solution

Concepts tested

• Rao-Blackwell Theorem
• Poisson Distribution
• Sufficient Statistic
• Unbiasedness

More questions from this set

• Exam MAS-I Practice Question 61
• Exam MAS-I Practice Question 63