Problem 1. Suppose that X and Y are independent standard normal. Show that o X and Y have zero correlation; o conditioned on the event X + Y Z 0, X and Y have negative correlation; o [3 bonus points] How about conditioned on the event X + Y Z t, Where t E R is arbitrary? Remark: In this emample you see that uncorrelated random variables may have negative correlation when conditioned on the event X + Y Z 0. This phenomenon is called Berk son's paradox which has several interesting interpretations in real life; see e.g. https: // en. wikipedia. org/wiki/BerksonZ27s_ paradoa