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PRMIA 8007 Exam Syllabus Topics:

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

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) a
B) 42
C) 1
D) a2

3. Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

A) 1.623
B) 0.377
C) 1.638
D) 2.362

4. Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

A) 2/5 and 1/2
B) 9/25 and 12/25
C) 2/5 and 3/5
D) 1/3 and 8/17

5. Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

A) negative
B) positive
C) zero
D) not defined

Solutions: