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

1. The natural logarithm of x is:

A) log(e)
B) always greater than x, for x>0
C) 46
D) the inverse function of exp(x)

2. If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

A) 3/4
B) 12/29
C) None of these
D) 37/45

3. Find the roots, if they exist in the real numbers, of the quadratic equation

A) 4 and -2
B) -4 and 2
C) 1 and 0
D) No real roots

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

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

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

Solutions: