Another poisson distribution question

[romeo6]

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!

 

[EnumaElish]

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.

 

[tacman]

Yes, that is correct. According to the Poisson distribution, the expected number of events in a given time interval is equal to the mean rate of events multiplied by the length of the interval. In this case, the mean time between events is 6 months, so the expected number of events in 18 months would be 3. Therefore, the most probable month for the third event to occur would be the 18th month. However, it is important to note that this is only a prediction based on the Poisson distribution and there is still a possibility for the event to occur in a different month.