4.1.概率分布列#

2025-11-07 10:09:17      世界杯巴西克罗地亚

根据定义可知:

\[\begin{eqnarray*}

P(X\leq 0.5) &=& P( X = -1)\\

&=& 0.25

\end{eqnarray*}\]

根据定义可知:

\[\begin{eqnarray*}

P(1.5 < X \leq 2.5) &=& P( X = 2)\\

&=& 0.5

\end{eqnarray*}\]

根据分布函数与分布列的关系可知:

当 \(x<-1\) 时, \(F(x) = P(X\leq x) = 0\) .

当 \(-1 \leq x < 2\) 时, \(F(x) = P(X\leq x) = P(X = -1) = 0.25\) .

当 \(2 \leq x < 3\) 时, \(F(x) = P(X\leq x) = P(X = -1) + P(X=2)= 0.75\) .

当 \(x \geq 3\) 时, \(F(x) = P(X\leq x) = P(X = -1) + P(X=2) + P(X=3)= 1\) .

综上,分布函数为

\[\begin{equation*}

F(x) =

\left\{

\begin{aligned}

& 0, && x < -1,\\

& 0.25, && -1 \leq x < 2,\\

& 0.75, && 2 \leq x < 3,\\

& 1, && x \geq 3.

\end{aligned}

\right.

\end{equation*}\]

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