Actuarial Notes

CAS Exam MAS-I Fall 2018, Question 40

Study guide: Exam MAS-I

A model is created with the following form:

f(x) = \beta_0 + \beta_1 x + \beta_2 x^2 + \beta_3 x^3 + \beta_4 (x - \xi)_+^3

where:

(x - \xi)_+^3 = (x - \xi)^3 \text{ if } x > \xi, \text{ and } 0 \text{ otherwise}

You are given the following statements:

  • I. f(x) is continuous at \xi
  • II. f'(x) is continuous at \xi
  • III. f''(x) is continuous at \xi

Determine which of the above statements are true.

  • A) I only
  • B) II only
  • C) III only
  • D) I, II, and III
  • E) The answer is not given by (A), (B), (C), or (D)

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