设随机变量(X)的概率密度函数(phi(x)=frac{1}{pi(1+x^2)})，求随机变量(Y=aX^2,(a < 0))的概率密度函数(f(y))

题目：设随机变量\(X\)的概率密度函数\(\phi(x)=\frac{1}{\pi(1+x^2)}\)，求随机变量\(Y=aX^2,(a < 0)\)的概率密度函数\(f(y)\)

A. \[ f(y)=\left\{ \begin{aligned} -\frac{1}{\pi(a+y)}\sqrt{\frac{a}{y}} &,& y < 0 \\ 0 &,& y \geq 0 \end{aligned} \right. \]

B. \[ f(y)=\left\{ \begin{aligned} -\frac{1}{\pi(a+y)}\sqrt{\frac{a}{2y}} &,& y < 0 \\ 0 &,& y \geq 0 \end{aligned} \right. \]

C. \[ f(y)=\left\{ \begin{aligned} -\frac{1}{\pi(a+y)}\sqrt{\frac{a}{2y}} &,& y > 0 \\ 0 &,& y \leq 0 \end{aligned} \right. \]

D. 以上答案均不正确

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