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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...

A) in the interval ]-,-2.5]
B) in the interval ]-2.5,-2[
C) equal to -2
D) in the interval ]-2,+[

2. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

A) [1, 2]
B) [0, 3]
C) [0, 1.5]
D) None of the above

3. There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds.
Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?

A) 0.5
B) None of these
C) 0.3
D) 0.6

4. The determinant of a matrix X is equal 2. Which of the following statements is true?

A) det(2X) = det(X)2
B) det(2X) =
C) det(2X) = 4 det(X)
D) det(2X) = 2 det(X)

5. The fundamental theorem of analysis establishes a relation between

A) First and second derivative of a function
B) Integration and differentiation of functions
C) The derivative of a function and the derivative of its inverse function
D) The derivative of a function and the slope of its graph

Solutions: