8002無料問題集「PRMIA PRM Certification - Exam II: Mathematical Foundations of Risk Measurement」

質問 1

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

（B）The normal distribution has higher kurtosis than the t distribution.

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

（D）The distributions have the same kurtosis.

正解：C 解答を投票する

質問 2

You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...

（A）in the interval ]-2,+[

（B）equal to -2

（C）in the interval ]-2.5,-2[

（D）in the interval ]-,-2.5]

正解：A 解答を投票する

質問 3

Consider the linear regression model for the returns of stock A and the returns of stock B.
Stock A is 50% more volatile than stock B.
Which of the following statements is TRUE?

（A）Beta must be positive ( )

（B）Alpha must be positive ( )

（C）The stocks must be positively correlated ( )

（D）Beta must be greater in absolute value than the correlation of the stocks ( )

正解：D 解答を投票する

質問 4

Which of the following statements are true about Maximum Likelihood Estimation?
(i)
MLE can be applied even if the error terms are not i.i.d. normal.
(ii)
MLE involves integrating a likelihood function or a log-likelihood function.
(iii)
MLE yields parameter estimates that are consistent.

（A）(i), (ii), and (iii)

（B）(i) and (ii)

（C）(i) only

（D）(i) and (iii)

正解：D 解答を投票する

質問 5

A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Modified Duration of the bond?

（A）1.75

（B）1.86

（C）2

（D）1.95

正解：B 解答を投票する

質問 6

What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?

（A）1 048 595

（B）2 097 172

（C）2 097 170

（D）1 048 574

正解：C 解答を投票する

質問 7

Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

（A）2/5 and 1/2

（B）9/25 and 12/25

（C）1/3 and 8/17

（D）2/5 and 3/5

正解：B 解答を投票する

質問 8

The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is

（A）(0, 0, 0)

（B）(1, 1, 1)

（C）(0, 2, 1)

（D）(0, 1, -1)

正解：D 解答を投票する

質問 9

Which of the following statements is true?

（A）Discrete and continuous compounding produce the same results if the discount rate is positive.

（B）Continuous compounding can be thought as making the compounding period infinitesimally small.

（C）The constant plays an important role in the mathematical description of continuous compounding.

（D）Continuous compounding is the better method because it results in higher present values compared to discrete compounding.

正解：B 解答を投票する

質問 10

The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

（A）f has necessarily neither a minimum nor a maximum at this point

（B）f has necessarily a maximum at this point

（C）f has necessarily a minimum at this point

（D）f might have either a minimum or a maximum or neither of them at this point

正解：D 解答を投票する

8002 無料問題集「PRMIA PRM Certification - Exam II: Mathematical Foundations of Risk Measurement」

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