(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]X(t)[/itex] is a Poisson process with [itex]\lambda=0.2[/itex] events per second. What is the probability of zero events in [itex]45[/itex] seconds?

2. The attempt at a solution

[itex]\frac{45}{0.2}=225[/itex] ([itex]0.2[/itex] second intervals)

so [itex]P[X=0][/itex] in [itex]225[/itex] consecutive intervals is:

[itex]\left(e^{-0.2}\right)^{225} = 2.86 \times 10^{-20}[/itex]

or

[itex]\lambda = (45)(0.2)=9[/itex] events per [itex]45[/itex] seconds gives:

[itex]e^{-9} = 1.23 \times 10^{-4}[/itex]

Both are approx. zero, but they are way different. How come?

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# Homework Help: Poisson Distribution - why are these different?

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