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Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Questions and Answers

Question 9

You want to test the hypothesis that a population parameter β of a regression model is zero. Your alternative hypothesis is that β≠0. Denote by SD(β) the estimated standard deviation of β, and by MEAN(β) the estimated mean of β. Which test statistic is appropriate, and what is its distribution?

Options:

A.

test statistic = SD(β)/MEAN(β), normal distribution

B.

test statistic = MEAN(β)/SD(β), normal distribution

C.

test statistic = SD(β)/MEAN(β), t distribution

D.

test statistic = MEAN(β)/SD(β), t distribution

Question 10

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?

Options:

A.

0.32

B.

0.64

C.

0.96

D.

1.92

Question 11

Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?

Options:

A.

N(0) = 0.5

B.

N'(0) ≥ 0

C.

N(x) → 0 as x → ∞

D.

N'(x) → 0 as x → ∞

Question 12

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?

Options:

A.

$2,208,972

B.

$2,210,342

C.

$2.205,000

D.

None of them

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Total 132 questions