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PRMIA 8007 Exam Syllabus Topics:

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

1. You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

A) b=0.5, a=2.5
B) b=2, a=4
C) b=2, a=0
D) b=0.5, a=1.5

2. 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) 2.50%
B) -5%
C) 5%
D) -2.50%

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

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

4. The bisection method can be used for solving f(x)=0 for a unique solution of x, when

A) The function f(x) is continuous and monotonic
B) The function f(x) is differentiable
C) The function f(x) is continuous
D) The function f(x) is differentiable and we have an explicit expression for the derivative

5. For a quadratic equation, which of the following is FALSE?

A) If the discriminant is zero, there is only one solution
B) If the discriminant is negative there are two different real solutions
C) If the discriminant is negative, there are no real solutions
D) If the discriminant is positive there are two different real solutions

Solutions: