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

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

2. 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

3. Which of the following properties is exhibited by multiplication, but not by addition?

A) associativity
B) commutativity
C) distributivity
D) invertibility

4. In statistical hypothesis tests, 'Type I error' refers to the situation in which...

A) Both null hypothesis and alternative hypothesis are rejected
B) The null hypothesis is accepted when in fact it should have been rejected
C) Both null hypothesis and alternative hypothesis are accepted
D) The null hypothesis is rejected when in fact it should have been accepted

5. Let N(.) denote the cumulative distribution function and suppose that X and Y are standard normally distributed and uncorrelated. Using the fact that N(1.96)=0.975, the probability that X 0 and Y 1.96 is approximately

A) 0.488%
B) 0.25%
C) 0.495%
D) 0.49%

Solutions: