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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) and (iii)
B) (i) and (ii)
C) (i), (ii), and (iii)
D) (i) only

2. Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A) 0
B) 1
C) 2
D) 3

3. What is the 40th term in the following series: 4, 14, 30, 52, ...?

A) 4598
B) 4960
C) 240
D) 4840

4. Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

A) F(x)g(x) - F(x)g'(x)dx
B) f(x)G(x) - F(x)g'(x)dx
C) F(x)g(x) + f(x)G(x)
D) F(x)G(x)

5. 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

Solutions: