设随机变量\(X\)的概率密度为\[ f(x)=\left\{ \begin{aligned} 1-|1-x| &,& 0 < x < 2 \\ 0 &,& others \\ \end{aligned} \right. \]求\(E(X)\)。
A. \(1\)
B. \(2\)
C. \(3\)
D. \(4\)
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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
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
(2)、若\(Y\)的分布函数为\(F(y)\)，则\(F(2)\)的值为
A. \(\frac{2}{5}\)
B. \(\frac{19}{30}\)
C. \(\frac{11}{30}\)
D. \(\frac{4}{15}\)
同时掷n颗均匀骰子，求它们的点数之和的数学期望
A. n/6
B. n
C. (3n)/2
D. (7n)/2
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