I have the following problem on my Statistics Problem Set:
I was able to use the multivariate Delta Method and solve items a) and b). However, I am struggling with items c) and d). Let me present my intuitions:
C) If $\mu_{X} = 0$, then the expected value of the ration of these two sample means is truly $\mu_{X}/\mu_{Y} = 0$ by the Law of Iterated Expectations. However, if this is not the case, Jensen's inequality kicks in and this won't hold anymore. However, I cannot go any further.
D) I have the impression that nothing can be said in this case with little information. I think that this thing won't converge to anything.
Any ideas? Thanks in advance!