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Exponential Distribution

Exponential Distribution

Плотность вероятности:

  • $f(x) = \left{ \begin{array}{lll} 0 & \mbox{if} & x < 0 \ \lambda e^{-\lambda x} & \mbox{if} & x \geqslant 0 \end{array} \right.$

  • $F(X) = \int_{-\infty}^{x} f(x) dx = \int_{-\infty}^{0} 0 dx + \lambda \int_{0}^{x} e^{-\lambda x} dx = 1 - e^{-\lambda x}$

Моменты

  • $M(X) = \frac{1}{\lambda}$
  • $D(X) = \frac{1}{\lambda^2}$
  • $M(X) = \sigma(X) = \frac{1}{\lambda}$