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

1. What can be said about observations of random variables that are i.i.d. a normally distributed?

A) The estimated mean divided by the estimated standard deviation has a Chi2-distribution
B) The estimated mean divided by the estimated standard deviation has a t-distribution
C) The estimated mean divided by the estimated variance has a Chi2-distribution
D) The estimated mean divided by the estimated variance has a t-distribution

2. The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A) 0
B) None of the above
C) 0.5
D) 1

3. You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?

A) test statistic = SD()/MEAN(), normal distribution
B) test statistic = MEAN()/SD(), normal distribution
C) test statistic = SD()/MEAN(), t distribution
D) test statistic = MEAN()/SD(), t distribution

4. An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?

A) 0.50
B) 0.02
C) 0.25
D) 0.14

5. Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

A) -1.2
B) None of the above
C) -2.8
D) 1.3

Solutions: