Correlation between two random input variables may change the mean of an output,but it will not affect the variability and shape of an output distribution.

Question

Quizplus · Accepted Answer

Correlation between two input variables can definitely affect the variability and shape of an output distribution. For example, if the two input variables are positively correlated, the output distribution may have a wider spread and longer tail than if the variables were uncorrelated. Conversely, negative correlation could lead to a narrower and more peaked output distribution.

Correlation Between Two Random Input Variables May Change the Mean