I have the following question regarding the conditional expectation of the ratio of two normal RVs and appreciate if anyone can help:
Let's assume $X \sim \mathcal{N}(\mu_x, \sigma_x^2)$ and $Y\sim \mathcal{N}(\mu_y, \sigma_y^2)$ are two independent normal RVs and $\frac{\mu_x}{\mu_y}=q$. Is it possible to calculate $\mathbb{E}(\frac{X}{Y} | X\geq Y$) as a function of $q$? If not possible, could a lower bound be defined for it as a function of $q$?
Thanks in advance for any tip or hint!