Let X and Y be two independent random variables uniformly distributed on (0,1). What is the expected value of their maximum? How does this expected value change if X and Y are perfectly positively correlated?

假设有两只互不相关的股票，它们未来一年的收益率X和Y独立且都服从(0,1)上的标准均匀分布。你的组合会挑表现更好的那只，这个最大值的期望收益是多少？如果宏观因素导致它们完全正相关，期望怎么变？