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

1. What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?

A) x ln(x) - x
B) ln(x) - x
C) exp(x)
D) 1/x

2. Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A) E(exp(X)) = 1.6487
B) E(exp(X)) = 0.6065
C) E(exp(X)) = 2.7183
D) E(exp(X)) = 1

3. Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data

A) Statements 1 and 3 are correct
B) All three statements are correct
C) Statements 1 and 2 are correct
D) Statements 2 and 3 are correct

4. Bond convexity is closely related to ...

A) The integral of the bond's present value with respect to yield
B) The derivative of the bond's present value with respect to yield
C) The second derivative of the bond's present value with respect to yield
D) The sensitivity of the bond's present value with respect to yield

5. 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) None of these
B) 0.3483
C) 0.2646
D) 0.7367

Solutions: