Actuarial Notes

CAS Exam MAS-II Spring 2019, Question 14

Study guide: Exam MAS-II

You are fitting a Linear Mixed Model to determine the effect of different preservatives on the shelf life of apples. You are given the following information:

  • Each apple is cut into three pieces and treated with a different preservative.
  • The measured between subject variance is 1.43 and the within subject variance is 0.87.

Determine which of the following matrices is the variance-covariance matrix for a randomly selected subject for the Implied Marginal Model.

  • A) \begin{bmatrix} 1.43 & 1.43 & 1.43 \\ 1.43 & 1.43 & 1.43 \\ 1.43 & 1.43 & 1.43 \end{bmatrix}
  • B) \begin{bmatrix} 0.87 & 0 & 0 \\ 0 & 0.87 & 0 \\ 0 & 0 & 0.87 \end{bmatrix}
  • C) \begin{bmatrix} 2.30 & 1.43 & 1.43 \\ 1.43 & 2.30 & 1.43 \\ 1.43 & 1.43 & 2.30 \end{bmatrix}
  • D) \begin{bmatrix} 0.87 & 1.43 & 1.43 \\ 1.43 & 0.87 & 1.43 \\ 1.43 & 1.43 & 0.87 \end{bmatrix}
  • E) \begin{bmatrix} 2.30 & 2.30 & 2.30 \\ 2.30 & 2.30 & 2.30 \\ 2.30 & 2.30 & 2.30 \end{bmatrix}

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