8007試験無料問題集（133題）「PRMIA Exam II: Mathematical Foundations of Risk Measurement

出題：1

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. All three statements are correct

B. Statements 2 and 3 are correct

C. Statements 1 and 3 are correct

D. Statements 1 and 2 are correct

正解：D 解答を投票する

出題：2

What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?

A. x ln(x) - x

B. 1/x

C. ln(x) - x

D. exp(x)

正解：A 解答を投票する

出題：3

Suppose that f(x) and g(x,y) are functions. What is the partial derivative of f(g(x,y)) with respect to y?

A. f(g(x,y)) dg/dy

B. f'(g(x,y)) dg/dy

C. f(dg/dy)

D. f'(g(x,y))

正解：B 解答を投票する

出題：4

The Newton-Raphson method

A. is based on Taylor series and uses the first derivative

B. is based on finding a middle point between left and right end of the search interval

C. does provide an error bound along with every iteration

D. can be used for continuous but not differentiable functions

正解：A 解答を投票する

出題：5

Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?

A. The distributions have the same kurtosis.

B. Which has the higher kurtosis depends on the degrees of freedom of the t distribution.

C. The normal distribution has lower kurtosis than the t distribution.

D. The normal distribution has higher kurtosis than the t distribution.

正解：C 解答を投票する

出題：6

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 0, variance is 2/3

C. mean is 0, variance is 1/2

D. mean is 1/3, variance is 1/3

正解：B 解答を投票する

出題：7

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

A. The probability that the estimated value of the parameter is within this interval is 95%.

B. The probability that the real value of the parameter is outside this interval is 95%.

C. The probability that the estimated value of the parameter is outside this interval is 95%.

D. The probability that the real value of the parameter is within this interval is 95%.

正解：D 解答を投票する

出題：8

A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?

A. 0.3333

B. 1.125

C. 0.75

D. 0.375

正解：D 解答を投票する

出題：9

Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

A. -2.8

B. -1.2

C. None of the above

D. 1.3

正解：B 解答を投票する

出題：10

Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A. Changing all the correlations to be zero

B. Changing the volatilities to be greater than 100%

C. All of the above

D. Changing all the correlations to be unity

正解：D 解答を投票する

8007試験無料問題集「PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition 認定」