Another poisson distribution question

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The discussion focuses on calculating the probability of the third event occurring in a Poisson distribution scenario where the mean time between events is 6 months. The most probable month for the third event is not necessarily the 18th month. To determine this, one must calculate the probability density function (p.d.f.) and the cumulative distribution function (c.d.f.) for the events. The relationship between the events is established through the c.d.f., which combines the probabilities of the first three events occurring within a specified time frame.

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romeo6
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Ok,

If the mean time between a single random event occurring is 6 months then is the most probably month for the third event to occur the 18th month?

Thanks!
 
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I don't know the answer but here's how I'd go about it. You need to calculate the probability density function (p.d.f.) of the third event occurring within a given time frame. Start from the basics, e.g. the corresponding cumulative distribution function (c.d.f.) will be Prob{third event < t} = Prob{event "one" < t and event "two" < t and event "three" < t} = Prob{event "one" < t} Prob{event "two" < t} Prob{event "three" < t}. Once you calculate the c.d.f., you can then figure out the p.d.f. The expected value of that p.d.f. is your answer.
 
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