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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
1. Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.
A) (i) only
B) (i) and (ii)
C) (i) and (iii)
D) (i), (ii), and (iii)
2. A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points
A) 24 basis point rise
B) 10 basis point rise
C) 24 basis fall
D) 30 basis points fall.
3. What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?
A) ln(x) - x
B) 1/x
C) exp(x)
D) x ln(x) - x
4. Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?
A) the definite integral of the CDF from minus infinity to plus infinity is undefined.
B) the CDF approaches 1 as its argument approaches infinity.
C) the definite integral of the PDF from minus infinity to plus infinity is zero.
D) the PDF is non-negative.
5. If a random variable X has a normal distribution with mean zero and variance 4, approximately what proportion of realizations of X should lie between -4 and +4?
A) 99%
B) 66.60%
C) 95%
D) 90%
Solutions:
| Question # 1 Answer: C | Question # 2 Answer: D | Question # 3 Answer: D | Question # 4 Answer: C | Question # 5 Answer: C |
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