I came across a question online which asks for $\limsup_{n\to\infty} Y_n$, given that $\mathbb{E}(\limsup_{n\to\infty} Y_n)=1$, where $\{Y_n\}$ is a sequence of independent r.v.s.
I cannot seem to figure this out. I have a feeling that the answer will be somewhat obvious, although I've tried many approaches, from Fatou's Lemma to Borel-Cantelli. Any help would be appreciated.