两个独立正态分布的随机变量的比值,服从怎样的分布?
设若X \sim N(\mu_X, \sigma_X^2)且Y \sim N(\mu_Y, \sigma_Y^2), 则其比值X/Y的分度密度由下式给出: f(t) = \frac{b_td_t}{a^3_t}\frac{1}{\sqrt{2 \pi}\sigma_X \sigma_Y} \Big( \Phi(b_t / a_t) - \Phi(-b_t / a_t) \Big) + \frac{1}{a^2_t \pi \sigma_X \sigma_Y}e^{-c/2}, 其中 a_t= \sqrt{t^2 / \sigma^2_X + 1/ \sigma^2_