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PRMIA 8007 Exam Syllabus Topics:

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

1. Calculate the determinant of the following matrix:

A) 2
B) 4
C) 4.25
D) -4.25

2. The fundamental theorem of analysis establishes a relation between

A) The derivative of a function and the derivative of its inverse function
B) Integration and differentiation of functions
C) The derivative of a function and the slope of its graph
D) First and second derivative of a function

3. Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

A) mean is 0, variance is 2/3
B) mean is 0, variance is 1/3
C) mean is 0, variance is 1/2
D) mean is 1/3, variance is 1/3

4. 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 = -1, y = 0
D) x = 0, y = 20

5. Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

A) f'(g(x,y))
B) f(dg/dy)
C) f(g(x,y)) dg/dy
D) f'(g(x,y)) dg/dy

Solutions: