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

1. 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 less than 1?

A) 0.64
B) 0.96
C) 0.32
D) 1.92

2. You invest $2m in a bank savings account with a constant interest rate of 5% p.a. What is the value of the investment in 2 years time if interest is compounded quarterly?

A) $2,210,342
B) None of them
C) $2.205,000
D) $2,208,972

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

4. You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

A) 42
B) 1
C) a2
D) a

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

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

Solutions: