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

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

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

2. In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

A) 6/11
B) 5/7
C) 8/11
D) None of these

3. 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,-2[
B) equal to -2
C) in the interval ]-,-2.5]
D) in the interval ]-2,+[

4. At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A) 2.66667
B) 2
C) -0.666666667
D) 0

5. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?

A) 0.96
B) 0.32
C) 1.92
D) 0.64

Solutions: