Let the population $U=(1,2,3)$. We want to estimate $R=\frac{\mu_y}{\mu_x}$.Consider the estimators $$\hat{R_1}=\frac{\overline{y}}{\overline{x}},\hat{R_2}=\frac{\overline{y}}{\mu_x}$$ where $Y=(9,42,53)$ and $X=(1,4,5)$.
Find the distributions of the estimators and their bias. Consider the sample size $n=2$
Considering a simple random sample without replacement, we have that $S=[(1,2),(1,3),(2,3)]$
$$\begin{bmatrix}s:&12&13&23\\\hat{R_1}: &10.2&10.33&10.55\\ p:&1/3&1/3&1/3 \end{bmatrix}$$
Just to ilustrate, taking $s=(1,2)$ I did $$\frac{\overline{y}}{\overline{x}}=\frac{(\frac{9+42}{2})}{(\frac{1+4}{2})}=10.2$$
but solutions say that the distribution is
$$\begin{bmatrix}s:&12&13&23\\\hat{R_1}: &0.098&0.097&0.095\\ p:&1/3&1/3&1/3 \end{bmatrix}$$
It is as if they had done $$\hat{R_1}=\frac{\overline{X}}{\overline{Y}}$$
Could anyone help me?