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

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

2. When the errors in a linear regression show signs of positive autocorrelation, which of the statements below is true?

A) The regression coefficient will be unbiased, but the standard error of the regression coefficient will be understated
B) The regression coefficient will be too low and the standard error of the regression coefficient will be overstated
C) The regression coefficient will be unbiased, but the standard error of the regression coefficient will be overstated
D) The regression coefficient will be too high and the standard error of the regression coefficient will be understated

3. Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter

A) (i), (ii), (iii), and (iv)
B) (i), (iii), and (iv)
C) (i) and (iv)
D) (i), (ii), and (iii)

4. The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

A) f has necessarily a maximum at this point
B) f has necessarily a minimum at this point
C) f has necessarily neither a minimum nor a maximum at this point
D) f might have either a minimum or a maximum or neither of them at this point

5. At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A) 2.66667
B) -0.666666667
C) 2
D) 0

Solutions: