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

1. The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A) 1
B) 0.5
C) 0
D) None of the above

2. Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A) F(x)g(x) + f(x)G(x)
B) F(x)G(x)
C) F(x)g(x) - F(x)g'(x)dx
D) f(x)G(x) - F(x)g'(x)dx

3. The gradient of a smooth function is

A) a matrix containing the function's second partial derivatives
B) matrix of second partial derivatives of a function
C) infinite at a maximum point
D) a vector that shows the direction of fastest change of a function

4. Two vectors are orthogonal when:

A) one is a scalar multiple of the other
B) their determinant is zero
C) their scalar product (sum product) is zero
D) their components are linearly dependent

5. Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

A) the definite integral of the CDF from minus infinity to plus infinity is undefined.
B) the PDF is non-negative.
C) the definite integral of the PDF from minus infinity to plus infinity is zero.
D) the CDF approaches 1 as its argument approaches infinity.

Solutions: