Actuarial Notes

CAS Exam MAS-I Spring 2018, Question 16

Study guide: Exam MAS-I

Suppose that a random draw is made from a normal distribution N(\mu, \sigma^2), where \sigma is known to be 2.

The normal distribution density is given by:

f(x; \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x-\mu)^2}{2\sigma^2}}, \qquad -\infty < x < \infty

Calculate the Fisher information of \mu.

  • 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

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