Question

Two independent variables are-

• A. Correlated
• B. Uncorrelated
• C. Linearly Correlated
• D. Nonlinearly Correlated

Hint:

Independence of variables always implies zero correlation, but zero correlation does not always imply independence.

Answer 1

The Correct Option is B

Step 1: Understanding independence.
Two variables are said to be independent if the occurrence of one variable does not affect the probability distribution of the other.
Step 2: Relation with correlation.
If two variables are independent, they do not show any type of correlation, whether linear or nonlinear.
Thus, independent variables are always uncorrelated.
Step 3: Analysis of options.
- (1) Correlated: Wrong, because independence means no relation.
- (2) Uncorrelated: Correct, independence = no correlation.
- (3) Linearly correlated: Wrong, this implies a straight-line relationship, which violates independence.
- (4) Nonlinearly correlated: Wrong, because correlation of any form indicates dependence.
Step 4: Conclusion.
Therefore, two independent variables are always uncorrelated.