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PRMIA 8007 Exam Syllabus Topics:

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

1. Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

A) mean is 0, variance is 1/3
B) mean is 1/3, variance is 1/3
C) mean is 0, variance is 2/3
D) mean is 0, variance is 1/2

2. 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), (ii), and (iii)
C) (i) and (iv)
D) (i), (iii), and (iv)

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

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 PDF from minus infinity to plus infinity is zero.
B) the definite integral of the CDF from minus infinity to plus infinity is undefined.
C) the CDF approaches 1 as its argument approaches infinity.
D) the PDF is non-negative.

5. When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

A) Take the square-root of 75 and raise it to the 5th power
B) Square 75, then take the fifth root of it
C) Multiply 75 by 2.5
D) Divide 75 by 2, then raise it to the 5th power

Solutions: