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I'm reading a proof and I don't understand one step.

1−(1−λ/n)^tn. Now, taking the limit as n→∞, P(Yn/n≤t)⟶1−e^(−λt). 

How does that work out? In this case, t is time(in seconds), n is the number of Bernoulli(p) trials per second and Yn is the time until the first success.

Further, if this converges to an exponential as n -> infinity, why is this significant?

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    Probably typo, want $1-\frac{\lambda}{n}$, not $1-\lambda n$.2012-11-04
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    sorry,didn't see that2012-11-04

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