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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
1. Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?
A) The distributions have the same kurtosis.
B) The normal distribution has lower kurtosis than the t distribution.
C) Which has the higher kurtosis depends on the degrees of freedom of the t distribution.
D) The normal distribution has higher kurtosis than the t distribution.
2. Find the roots, if they exist in the real numbers, of the quadratic equation
A) No real roots
B) -4 and 2
C) 4 and -2
D) 1 and 0
3. What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?
A) (x + y) / (x+y)
B) ln(x+y) x + ln(x+y) y
C) 1 / (x+y)
D) -x/(x+y) - y/(x+y)
4. Variance reduction is:
A) A method for reducing the number of simulations required in a Monte Carlo simulation
B) A numerical method for finding the variance of the underlying that is implicit in a market price of an option
C) A technique that is applied in regression models to improve the accuracy of the coefficient estimates
D) A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
5. Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in
[0,4]?
A) 1/4 and 1/6
B) None of the above
C) 1/7 and 1/9
D) 1/4 and 1/7
Solutions:
| Question # 1 Answer: B | Question # 2 Answer: A | Question # 3 Answer: A | Question # 4 Answer: A | Question # 5 Answer: B |





