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

1. 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

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

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

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

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

4. Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A) f(x)G(x) - F(x)g'(x)dx
B) F(x)G(x)
C) F(x)g(x) + f(x)G(x)
D) F(x)g(x) - F(x)g'(x)dx

5. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

A) f has necessarily neither a minimum nor a maximum at this point
B) f has necessarily a minimum at this point
C) f might have either a minimum or a maximum or neither of them at this point
D) f has necessarily a maximum at this point

Solutions: