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Intermediate Proof

Derivation of the Exponential Distribution from a Poisson Process

Students often struggle with the transition from the discrete Poisson probability mass function to the continuous Exponential density function. The common mistake is failing to recognize that the event {T>t} \{T > t\} is equivalent to the Poisson state N(t)=0 N(t) = 0 for the same interval.
Institutional Reference: Applied Statistics
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