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

1. Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

A) 0.5
B) 0
C) 2
D) 1

2. What is the maximum value for f(x)= 8-(x+3)(x-3)?

A) -1
B) 17
C) 8
D) None of these

3. 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 1/7
B) 1/7 and 1/9
C) 1/4 and 1/6
D) None of the above

4. I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price 100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to 90 and the price of stock 2 rises to 150, what is the return on my portfolio?

A) 5%
B) 2.50%
C) -5%
D) -2.50%

5. The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A) x = 5, y = 0
B) None of the above
C) x = 0, y = 20
D) x = -1, y = 0

Solutions: