hard · FRM Part 1 Quantitative Analysis
X and Y are each standard normal with linear correlation ρ = 0. An analyst concludes they are independent and that the tail-dependence in a stress scenario is therefore zero.
Under which single additional assumption is the analyst's independence conclusion guaranteed correct, and why does ρ=0 alone fail?
- Correct only if (X,Y) is jointly (bivariate) normal; zero correlation alone permits dependence such as Y=X^2-type structure where ρ=0 yet X and Y are clearly dependent.
- Correct unconditionally: for standard normal margins, zero linear correlation always implies full statistical independence.
- Correct only if X and Y have finite fourth moments; zero correlation plus finite kurtosis is sufficient for independence.
- Correct only if Spearman's rank correlation is also zero; matching Pearson and Spearman correlations of zero implies independence for any margins.
Sign up free to see the explanation and track your rank →
More FRM Part 1 Quantitative Analysis practice
- A probability distribution that is asymmetric and has a significantly long tail extending
- A single discrete trial that results in exactly one of two possible outcomes (success or f
- How does the mean of a lognormal distribution compare to the mean of its associated normal
- If an analyst says a return series has 'fat tails,' what does this imply for a risk model
- If the correlation between two assets is -1.0, what does this indicate about their co-move
- In Bayesian inference, what does the term 'Updating' refer to?
- In combinatorics, which coefficient represents the number of ways to select r items from a
- In the context of credit risk, if D is the event of default and F is a model flag, how is