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5.4: 章节公式回顾

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    204879

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    5.1 连续概率密度函数的属性

    概率密度函数 (pdf)\(f(x)\)：

    • 累积分布函数 (cdf)：\(P(X \leq x)\)

      5.2 均匀分布

      \(X \sim U (a, b)\)

      平均值是\(\mu=\frac{a+b}{2}\)

      标准差为\(\sigma=\sqrt{\frac{(b-a)^{2}}{12}}\)

      概率密度函数：\(f(x)=\frac{1}{b-a} \text { for } a \leq X \leq b\)

      左侧区域\(\bf{x}\)：\(P(X<x)>

      \ (\ bf {x}\) 右侧的区域：\(P(X>x)=(b-x)\left(\frac{1}{b-a}\right)\)

      介于\(\bf{c}\)和之间的区域\(\bf{d}\)：\(P(c<d)>

      • 5.3 指数分布

        • pdf:\ (f (x) = me^ {(—mx)}\) where\(x \geq 0\) and\(m > 0\)
        • cdf:\(P(X \leq x) = 1 – e^{(–mx)}\)
        • 意思\(\mu = \frac{1}{m}\)
        • 标准差\(\sigma = \mu\)
        • 此外
          • \(P(X > x) = e^{(–mx)}\)
          • \(P(a < X < b) = e^{(–ma)} – e^{(–mb)}\)
        • 泊松概率：\(P(X=x)=\frac{\mu^{x} e^{-\mu}}{x !}\)均值和方差为\(\mu\)