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

2. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) 42
B) 1
C) a2
D) a

3. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

A) f has necessarily a maximum at this point
B) f has necessarily a minimum at this point
C) f might have either a minimum or a maximum or neither of them at this point
D) f has necessarily neither a minimum nor a maximum at this point

4. 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)) = 2.7183
B) E(exp(X)) = 0.6065
C) E(exp(X)) = 1.6487
D) E(exp(X)) = 1

5. When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

A) 25
B) 5
C) 10
D) 100

Solutions: