过点((0,1))任意作直线与(x)轴正向成角(alpha),(alpha)在((0,pi))上均匀分布,求该直线在(x)轴的截距的概率密度函数(f(x))

lk2025-03-14  5

题目:过点\((0,1)\)任意作直线与\(x\)轴正向成角\(\alpha\),\(\alpha\)在\((0,\pi)\)上均匀分布,求该直线在\(x\)轴的截距的概率密度函数\(f(x)\)

A. \[ f(x)=\frac{2}{\pi(4+x^2)},-\infty < x < +\infty \]

B. \[ f(x)=\frac{3}{\pi(9+x^2)},-\infty < x < +\infty \]

C. \[ f(x)=\frac{4}{\pi(16+x^2)},-\infty < x < +\infty \]

D. 以上答案均不正确

答案:评论后可见此内容

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