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

1. A 95% confidence interval for a parameter estimate can be interpreted as follows:

A) The probability that the real value of the parameter is outside this interval is 95%.
B) The probability that the real value of the parameter is within this interval is 95%.
C) The probability that the estimated value of the parameter is within this interval is 95%.
D) The probability that the estimated value of the parameter is outside this interval is 95%.

2. For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)

A) convex, convex, concave
B) concave, convex, convex
C) convex, concave, concave
D) concave, concave, concave

3. Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A) geometric sequence, common ratio 3
B) arithmetic sequence, common ratio 2
C) arithmetic sequence, common difference 2
D) geometric sequence, common ratio 2

4. Which of the following statements about skewness of an empirical probability distribution are correct?
1. When sampling returns from a time series of asset prices, discretely compounded returns exhibit higher skewness than continuously compounded returns
2. When the mean is significantly less than the median, this is an indication of negative skewness
3. Skewness is a sign of asymmetry in the dispersion of the data

A) Statements 1 and 2 are correct
B) Statements 1 and 3 are correct
C) Statements 2 and 3 are correct
D) All three statements are correct

5. Which of the following statements concerning class intervals used for grouping of data is correct?
When grouping data, attention must be paid to the following with regards to class intervals:
1. Class intervals should not overlap
2. Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup
3. The class intervals should be large enough so that they not obscure interesting variation within the group

A) Statements 1 and 2 are correct
B) Statements 1 and 3 are correct
C) Statements 2 and 3 are correct
D) All three statements are correct

Solutions: