In the last few posts we have been looking at the properties of memoryless processes, being those processes that trigger events at intervals that are independent of how long we have been waiting for one to happen. First we answered the question of what is the probability that we must wait some given time that an event will occur with the exponential distribution, and then the question of what is the probability that we must wait some given time for the *k*^{th} event to occur with the gamma distribution, which allows the somewhat counter-intuitive case of non-integer *k*.

This time I'd like to ask another question; what is the probability that we'll observe *k* events, occurring at a rate *λ*, in a period of one unit of time?

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