This elementary exercise is intended to give an example showing that lack of correlation does not necessarily mean independence!
Let us assume that X ∼ N(0, 1) and let us define the random variable Y by:
![](https://book.transtutors.com/qimg/bd80e789-831b-4fdb-9061-1983c4509561.png)
1. Compute 𝔼{|X|}
2. Show that Y has mean zero, variance 1, and that it is uncorrelated with X.