FRM Quantitative Analysis 1

Question 1

In a normal distribution, approximately what percentage of observations fall within two standard deviations of the mean?

Accepted Answer

95%

Answer

Approximately 95% of observations fall within ±2 standard deviations in a normal distribution, following the empirical 68-95-99.7 rule.

Question 2

Which statistical measure describes the asymmetry of a probability distribution?

Accepted Answer

Skewness

Answer

Skewness measures the asymmetry of a distribution, with positive skewness indicating a longer right tail and negative skewness indicating a longer left tail.

Question 3

A leptokurtic distribution compared to a normal distribution has:

Accepted Answer

Excess kurtosis greater than 0

Answer

A leptokurtic distribution has excess kurtosis greater than 0 (kurtosis > 3), indicating heavier tails and a higher peak than a normal distribution, which is critical for risk modeling.

Question 4

The covariance between two assets is 0.006, and their standard deviations are 0.10 and 0.15. What is their correlation coefficient?

Accepted Answer

0.40

Answer

Correlation = Covariance / (σ1 × σ2) = 0.006 / (0.10 × 0.15) = 0.006 / 0.015 = 0.40.

Question 5

Which statement best describes the Central Limit Theorem (CLT)?

Accepted Answer

The distribution of sample means approaches normality as sample size increases regardless of the underlying distribution

Answer

The CLT states that the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population's underlying distribution.

FRM Practice Test

FRM Practice Test

FRM Quantitative Analysis 1