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

1. Which of the provided answers solves this system of equations?
2y - 3x = 3y +x
y2 + x2 = 68

A) x = 1; y = square root of 67
B) x = 2; y = 8
C) x = 2; y = -8
D) x = -2; y = -8

2. The natural logarithm of x is:

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

3. Which of the following is consistent with the definition of a Type I error?

A) A Type I occurs whenever data series are serially correlated
B) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of positive correlation was rejected
C) The probability of a Type I error is 100% minus the significance level
D) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of no correlation was rejected

4. Maximum likelihood estimation is a method for:

A) Finding parameter estimates of a given density function
B) Estimating the implied volatility of a simple European option
C) Estimating the solution of a partial differential equation
D) Solving a portfolio optimization problem

5. 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=2, a=4
B) b=2, a=0
C) b=0.5, a=2.5
D) b=0.5, a=1.5

Solutions: