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PRMIA 8007 Exam Syllabus Topics:

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

1. In statistical hypothesis tests, 'Type I error' refers to the situation in which...

A) Both null hypothesis and alternative hypothesis are rejected
B) Both null hypothesis and alternative hypothesis are accepted
C) The null hypothesis is rejected when in fact it should have been accepted
D) The null hypothesis is accepted when in fact it should have been rejected

2. Calculate the determinant of the following matrix:

A) 2
B) 4
C) -4.25
D) 4.25

3. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

A) 0.125
B) -2.5
C) -1.25
D) 2.5

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

5. 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) 2
B) 0
C) 3
D) 1

Solutions: