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

1. If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?

A) 90%
B) 95%
C) 66.60%
D) 99%

2. An indefinite integral of a polynomial function is

A) always positive
B) none of the above
C) always increasing
D) always less than the function itself

3. 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) 1/3 and 8/17
D) 2/5 and 3/5

4. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

A) None of the above
B) [0, 3]
C) [0, 1.5]
D) [1, 2]

5. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

A) 0.5292
B) 0.5288
C) 0.5290
D) 0.5286

Solutions: