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Suppose...

$ X\sim B(1,p_x)~~~~~~~~~\bar X\sim N(p_x,\frac{p_x(1-p_x)}{n_x})\\ Y\sim B(1,p_y)~~~~~~~~~~\bar Y\sim N(p_y,\frac{p_y(1-p_y)}{n_y})\\ $

How can we estimate $\frac{p_x}{p_y}$? Or what is the expectation and variance of $\frac{\bar X}{\bar Y},$ $E(\frac{\bar X}{\bar Y})$ and $Var(\frac{\bar X}{\bar Y})$?

bbbbbliu
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    Parts of your question make no sense. In particular, since $p_x$ and $p_y$ are parameters--not random variables--you don't estimate them; you just compute their ratio. Although you introduce random variables $X$ and $Y$, you never use them or ask about them. This all suggests you haven't succeeded in asking what you intended to ask. Could you please clarify your question? – whuber Aug 24 '17 at 17:37
  • Actually it relates to the question I asked few days ago: https://stats.stackexchange.com/questions/299130/test-for-significant-difference-in-ratios-of-sample-means?noredirect=1#comment568711_299130 Sorry for my poor statistics concept, why would we not estimate parameters? Am I wrong saying that sample mean is to estimate the true mean? – bbbbbliu Aug 24 '17 at 17:44
  • That's not at all clear, because that question does not refer to $X$, $Y$, $p_x$, or $p_y$. Please edit your post here so that it won't be misinterpreted. – whuber Aug 24 '17 at 17:48
  • Since when is the sample mean of Bernoulli rv Normal? – wolfies Aug 24 '17 at 18:29

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