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

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

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

2. I have a portfolio of two stocks. The weights are 60% and 40% respectively, the volatilities are both 20%, while the correlation of returns is 100%. The volatility of my portfolio is

A) 24%
B) 14.4%
C) 4%
D) 20%

3. Two vectors are orthogonal when:

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

4. A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A) 0.3483
B) 0.7367
C) None of these
D) 0.2646

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) 1.92
B) 0.96
C) 0.64
D) 0.32

Solutions: