Kendall’s tau rank correlation between X and Y is 0.55. Both X and Y are positive. What is Kendall’s tau between X and 1/Y ? What is Kendall’s tau between 1/X and 1/Y ? Suppose that X is Uniform(0,1)...

Kendall’s tau rank correlation between X and Y is 0.55. Both X and Y are positive. What is Kendall’s tau between X and 1/Y ? What is Kendall’s tau between 1/X and 1/Y ?

Suppose that X is Uniform(0,1) and Y = X2. Then the Spearman rank correlation and the Kendall’s tau between X and Y will both equal 1, but the Pearson correlation between X and Y will be less than 1. Explain why.