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 $Var(\frac{\bar X}{\bar Y})$?