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I have Propability function that has caused me some trouble.

X is a stochastic variable which is Poisson distributed with the parameter

[tex] \lambda > 0[/tex]

The Propability function is therefore:

[tex]

P(X=x) = \left\{ \begin{array}{ll}

\frac{{e^{- \lambda}{\lambda ^{x}}}}{{x!}} & \textrm{where} \ x \in (0,1,2,\ldots)&\\

0 & \textrm{other.}&\\

\end{array} \right.

[/tex]

I'm suppose to show

[tex]P(X \geq 1) = 1 - e^{- \lambda}[/tex]

(step1) I get by inserting into the top formula

[tex]P(X=1) = \lambda e ^ {- \lambda}[/tex]

My question is how do go from P(X=1) to [tex] P(X \geq 1) [/tex] ???

Sincerley

Fred

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# Homework Help: Propability function Question

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