Financial Risk Manager Part 1
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Which of the following statements is false?
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NNikitesh
A
Correlation and covariance measure the strength of the linear relationship between two variables
B
Mathematically, we determine correlation by dividing the covariance between two random variables by the product of their standard deviations
C
Two variables are independent if the knowledge of one variable does not impact the probability distribution of the other variable
D
If two variables have a correlation of zero, this implies they also have zero dependence between them
Explanation:
Explanation:
Statement D is false because correlation measures only linear relationships between variables. A correlation of zero indicates no linear relationship, but there could still be non-linear dependencies between the variables.
Key points:
- Correlation (ρ) = Cov(X,Y) / (σ_X × σ_Y)
- Correlation = 0 means no linear relationship
- Dependence ≠ 0 could still exist through non-linear relationships
- Independence implies correlation = 0, but correlation = 0 does NOT imply independence
Examples of zero correlation but non-zero dependence:
- X ~ Uniform(-1,1), Y = X² → Correlation = 0 but clear quadratic relationship
- Circular relationships where points form a circle pattern
- Other non-linear functional relationships
Correct statements:
- A: True - Both measure linear relationship strength
- B: True - This is the mathematical definition of correlation
- C: True - This is the definition of statistical independence
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